# Two air track carts move toward one another on an air track. Cart 1 has a mass of 0.55 kg and a speed of 1.0 m/s. Cart 2 has a mass of 0.51 kg

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### Physics

Two air-track carts move toward one another on an air track. Cart 1 has a mass of 0.336 kg and a speed of 1.16 m/s. Cart 2 has a mass of 0.634 kg. What speed must cart 2 have if the total momentum of the system is is to be zero? What is the system's kinetic energy?

### physics (fixed)

Two air-track carts move toward one another on an air track. Cart 1 has a mass of 0.34 kg and a speed of 1.1 m/s . Cart 2 has a mass of 0.68 kg and a speed of 0.55 m/s. Calculate the system's kinetic energy.

### physics

Two air-track carts move toward one another on an air track. Cart 1 has a mass of 0.34 kg and a speed of 1.1 m/s . Cart 2 has a mass of 0.68 kg and a speed of 0.55 m/s .

### physics

two air carts of mass m1=0.87kg and m2=0.48kg are placed on a frictionless track.cart 1 is at rest initally, and a spring bumper with a force constant of 690N/m. cart 2 has a flat metal surface for a bumper, and move toward the bumper of the stationary cart with an intial ...

### Physics

two air carts of mass m1=0.87kg and m2=0.48kg are placed on a frictionless track.cart 1 is at rest initally, and a spring bumper with a force constant of 690N/m. cart 2 has a flat metal surface for a bumper, and move toward the bumper of the stationary cart with an intial ...

### physics

An air-track cart with mass m=0.20kg and speed v0=1.5m/s approaches two other carts that are at rest and have masses 2m and 3m, as indicated in (Figure 1) . The carts have bumpers that make all the collisions elastic. Find the final speed of cart 1, assuming the air track ...

### Physics

W have three air carts (labeled #1, #2, and #3) on an air track. The carts are equipped with spring bumpers so that all collisions are elastic. The masses of the carts are m1 = 5m, m2 = 2m, and m3 = m. Initially, cart #1 is given a velocity to the right of magnitude v0 and the...

### Physics

An air-track cart of mass 0.10 is moving with a speed 1.2 to the right when it collides with a cart of mass 0.24 that is at rest. Each cart has a wad of putty on its bumper, and hence they stick together as a result of their collision. Suppose the average contact force between...

### physics

A block of mass M1 = 0.320 kg is initially at rest on a cart of mass M2 = 0.680 kg with the cart initially at rest on a level air track. The coefficient of static friction between the block and the cart is ?s = 0.610, but there is essentially no friction between the air track ...

### Physics Classical Mechanics

The figure below shows the experimental setup to study the collision between two carts. In the experiment cart A rolls to the right on the level track, away from the motion sensor at the left end of the track. Cart B is initially at rest. The mass of cart A is equal to the ...

### Physics -Conservation of Momentum-

1) A 1 kg mass moving at 1 m/s has a totally inelastic collision with a 0.7 kg mass. What is the speed of the resulting combined mass after the collision? 2) A cart of mass 1 kg moving at a speed of 0.5 m/s collides elastically with a cart of mass kg at rest. The speed of the ...

### Physics -Conservation of Momentum-

1) A 1 kg mass moving at 1 m/s has a totally inelastic collision with a 0.7 kg mass. What is the speed of the resulting combined mass after the collision? 2) A cart of mass 1 kg moving at a speed of 0.5 m/s collides elastically with a cart of mass kg at rest. The speed of the ...

### Physics 1

A cart with mass 340 g moving on a frictionless linear air track at an initial speed of 1.5 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision, the first cart continues in its original direction at 0.42 m/s. (a) What is ...

### Physics ~really need help!~

1) A 1 kg mass moving at 1 m/s has a totally inelastic collision with a 0.7 kg mass. What is the speed of the resulting combined mass after the collision? 2) A cart of mass 1 kg moving at a speed of 0.5 m/s collides elastically with a cart of mass kg at rest. The speed of the ...

### physics

A cart of mass 223 g is placed on a frictionless horizontal air track. A spring having a spring constant of 10.20 N/ m is attached between the cart and the left end of the track. When in equilibrium, the cart is located 11.0 cm from the left end of the track. If the cart is ...

### physics

A cart of mass 223 g is placed on a frictionless horizontal air track. A spring having a spring constant of 10.20 N/ m is attached between the cart and the left end of the track. When in equilibrium, the cart is located 11.0 cm from the left end of the track. If the cart is ...

### physics

A 1.92 kg cart and a 3.7 kg cart both slide toward each other at 1.34 m/s on an air track. They collide and stick. The combined mass moves at what speed in m/s

### Physics

A 3.0-kg cart is rolling along a frictionless, horizontal track towards a 1.2-kg cart that is held initially at rest. The carts are loaded with strong magnets that cause them to attract one another. Thus, the speed of each cart increases. At a certain instant before the carts ...

### physics

A 2.4-kg cart is rolling along a frictionless, horizontal track towards a 1.3-kg cart that is held initially at rest. The carts are loaded with strong magnets that cause them to attract one another. Thus, the speed of each cart increases. At a certain instant before the carts ...

### physics

A 2.9-kg cart is rolling along a frictionless, horizontal track towards a 1.5-kg cart that is held initially at rest. The carts are loaded with strong magnets that cause them to attract one another. Thus, the speed of each cart increases. At a certain instant before the carts ...

### physics

A cart of mass 223 g is placed on a frictionless horizontal air track. A spring having a spring constant of 10.20 N/ m is attached between the cart and the left end of the track. When in equilibrium, the cart is located 11.0 cm from the left end of the track. If the cart is ...

### physics

A 0.054-kg pet lab mouse sits on a 0.35-kg air-track cart, as shown in (Figure 1) . The cart is at rest, as is a second cart with a mass of 0.25 kg. The lab mouse now jumps to the second cart. After the jump, the 0.35-kg cart has a speed of v1=0.80m/s. What is the speed v2 of ...

### physic

Six roller-coaster carts pass over the same semicircular "bump." The mass M of each cart (including passenger) and the normal force n of the track on the cart at the top of each bump are given in the figures. Iam given the force in N of the cart at the peak of the loop and the...

### physics

A cart of mass 340 g moving on a frictionless linear air track at an initial speed of 1.2 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision the first cart continues in its original direction at .66m/s. a) what is the mass...

### pals help

An air-track cart with mass m1=0.29kg and initial speed v0=0.95m/s collides with and sticks to a second cart that is at rest initially. Part A If the mass of the second cart is m2=0.55kg, how much kinetic energy is lost as a result of the collision?

### Physics Help

A small, 200 g cart is moving at 1.50 m/s on an air track when it collides with a larger, 2.00 kg cart at rest. After the collision, the small cart recoils at 0.890 m/s. Q: What is the speed of the large cart after the collision? How do you set this up? Would it be like (mass ...

### physics

Two carts are involved in an elastic collision. Cart A with mass 0.55 kg is moving towards Cart B with mass 0.55 kg, which is initially at rest. Cart A stops after the collision and Cart B begins to move. What is the final kinetic energy of Cart B?

### physics

The drawing below shows two laboratory carts (each has a mass of 1.0 kg) X and Y in contact with a compressed exploder spring between them. The mass on cart Y is 2.33 kg, distance A is 6 cm, distance B is 9 cm. What mass must be placed on cart X, such that after the explosion ...

### Physics

A cart of mass m1 = 12 kg slides down a frictionless ramp and is made to collide with a second cart of mass m2 = 21 kg, which then heads into a vertical loop of radius 0.26 m, but the carts stick together after the collision.Find the height h from which cart 1 would need to ...

### Physics

A 5000 kg cart carrying a vertical rocket launcher moves to the right at a constant speed of 27.0 m/s along a horizontal track. It launches a 54.8 kg- rocket vertically upward with an initial speed of 33.1 m/s relative to the cart. A) where will the rocket land, relatively to ...

### Physics

Suppose now that the air carts below are both moving to the right initially. The cart to the left has a mass m1 and an initial speed v0; the cart to the right has an initial speed v0/2. If the center of mass of this system moves to the right with a speed 6/7 multiplied by v0, ...

### Physics

As shown in the figure below, we have three air carts (labeled #1, #2, and #3) on an air track. The carts are equipped with spring bumpers so that all collisions are elastic. The masses of the carts are m1 = 5m, m2 = 2m, and m3 = m. Initially, cart #1 is given a velocity to ...

### Physics

At the top of an inclined track, a spring is attached to a rod at one end and a dynamics cart at the other such that the spring stretches parallel to the track. The cart has a mass of .850kg and there is negligible friction between the cart and the track. The spring has a ...

### physics

A cart on a horizontal, linear track has a fan attached to it. The cart is positioned at one end of the track, and the fan is turned on. Starting from rest, the cart takes 4.22 s to travel a distance of 1.44 m. The mass of the cart plus fan is 350 g. Assume that the cart ...

### physics-momentum HELP PLEASE tesst in two days

A student flings a 2.3g ball of putty at a 225g cart sitting on a slanted air track that is 1.5m long. The track is slanted at an angle of 25 degrees with the horizontal. If the putty is travelling at 4.2 m/s when it hits the cart, will the cart reach the end of the track ...

### Physics

Suppose now that the air carts below are both moving to the right initially. The cart to the left has a mass m1 and an initial speed v0; the cart to the right has an initial speed v0/2. If the center of mass of this system moves to the right with a speed 6/7 v0, what is the ...

### PHYSICS

A roller coaster powered by a spring launcher follows a frictionless track as shown below. The roller coaster cart has a mass of 500 kg, and the spring launcher has a spring constant of 1500 N/m. a. If the cart starts at a height h1 = 10m, how much must the spring be ...

### physics

A student flings a 2.3g ball of putty at a 225g cart sitting on a slanted air track that is 1.5m long. The track is slanted at an angle of 25 degrees with the horizontal. If the putty is travelling at 4.2 m/s when it hits the cart, will the cart reach the end of the track ...

### Physics - Momentum

A student flings a 2.3g ball of putty at a 225g cart sitting on a slanted air track that is 1.5m long. The track is slanted at an angle of 25 degrees with the horizontal. If the putty is travelling at 4.2 m/s when it hits the cart, will the cart reach the end of the track ...

### physics

A 350-g air track cart on a horizontal air track is attached to a string that goes over a pulley with a moment of inertia of 6.00 × 10-6 kg·m2 and a radius of 1.35 cm. The string is pulled vertically downward by a force of 2.50 N. What is the acceleration of the cart?

### Physics - elastic collision

A student flings a 23g ball of putty at a 225g cart sitting on a slanted air track that is 1.5m long. The track is slanted at an angle of 25deg with the horizontal. If the putty is traveling at 4.2m/s when it hits the cart, will the cart reach the end of the track before it ...

### Physics

Cart A has a mass of 10kg and is moving towards cart B at a speed of 15 m/s. If cart B is moving towards cart A with a speed of 5 m/s, what mass must Cart B have to stop both carts upon collision?

### PHYSICS

A Few questions- please help!!! also show steps! What magnitude of force, acting for 0.025 s, will change the velocity of a 100 g ball from 30 m/s eastward to 40 m/s westward? A girl holds a 1.7 kg air rifle loosely and fires a bullet of mass 2 g. The muzzle velocity of the ...

### Physics

Three dynamics carts have force sensors placed on top of them.(cart 1, with mass of 2.2 kg, has one sensor --> cart 2, with mass of 2.5 kg, has sensors two and then three --> cart 3, with mass of 1.8 kg, has sensors four then five). Each force sensor is tied to a string ...

### Help ?

Two carts, A and B, are connected by a rope 39 ft long that passes over a pulley P (see the figure). The point Q is on the floor h = 12 ft directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 3.5 ft/s. How fast is cart B moving toward Q at...

### physics

A cart of mass 340 g moving on a frictionless linear air track at an initial speed of 1.2 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision the first cart continues in its original direction at .66m/s. a) what is the mass...

### physics

A small, 300g cart is moving at 1.60m/s on an air track when it collides with a larger, 2.00kg cart at rest. After the collision, the small cart recoils at 0.820m/s. What is the speed of the large cart after the collision?

### physics

Two carts of equal mass, m = 0.280 kg, are placed on a frictionless track that has a light spring of force constant k = 51.9 N/m attached to one end of it. The red cart is given an initial velocity of v0 = 3.50 m/s to the right, and the blue cart is initially at rest. If the ...

### physics

A small, 300 g cart is moving at 1.90 m/s on an air track when it collides with a larger, 2.00 g cart at rest. After the collision, the small cart recoils at 0.820 m/s. What is the speed of the large cart after the collision?

### Calculus Help Please!!!

Two carts, A and B, are connected by a rope 39 ft long that passes over a pulley P (see the figure). The point Q is on the floor h = 12 ft directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 3.5 ft/s. How fast is cart B moving toward Q at...

### Physics

Two carts, one twice as heavy as the other, are at rest on a horizontal frictionless track. A person pushes each cart with the same force for 6.00 s. If the kinetic energy of the lighter cart after the push is K, the kinetic energy of the heavier cart is A. 1/4 K B. 1/2 K C. K...

### physics

Two carts, one twice as heavy as the other, are at rest on a horizontal frictionless track. A person pushes each cart with the same force for 4.00 s. If the magnitude of the momentum of the lighter cart after the push is P, the magnitude of the momentum of the heavier cart is ...

### physics

Two carts, one twice as heavy as the other, are at rest on a horizontal frictionless track. A person pushes each cart with the same force for 4.00 s. If the magnitude of the momentum of the lighter cart after the push is P, the magnitude of the momentum of the heavier cart is ...

### physics

Two carts, one twice as heavy as the other, are at rest on a horizontal frictionless track. A person pushes each cart with the same force for 6.00 s. If the kinetic energy of the lighter cart after the push is K, the kinetic energy of the heavier cart is A. 1/4 K B. 1/2 K C. K...

### physics

one car of mass 15.0kg is moving 5.00m/s to the right on a frictionless track and collides with a cart of mass 3.00kg. the final velocity of the carts that become stuck together after the collision is 1.50m/s to the right. find the velocity of the second cart before the ...

### Momentum Problem

A cart of mass m1 = 15 kg slides down a frictionless ramp and is made to collide with a second cart of mass m2 = 23 kg which then heads into a vertical loop of radius 0.21 m. (a) Determine the height h at which cart #1 would need to start from to make sure that cart #2 ...

### Physics

In a supermarket parking lot, an employee is pushing ten empty shopping carts, lined up in a straight line. The acceleration of the carts is 0.080 m/s2. The ground is level, and each cart has a mass of 25 kg. (a) What is the net force acting on any one of the carts? N (b) ...

### Physic

A 220 g cart moves on an air track (a one-dimensional system in which motion is friction free) at 1.3 m/s. It collides with and sticks to another cart of mass 550 g, which was moving in the opposite direction at 0.80 m/s before the collision. What is the velocity of the ...

### Physics

Two boys standing on carts that move along a horizontal frictionless surface. The mass of each boy-cart combination is 100 kg, and each moves initially with the velocities of: Boy A 7cm/sec and Boy B: 10cm/sec. The boy on cart A throws a 2kg ball to the boy on Cart B (assume ...

### physics

Two air-track carts are sliding to the right at 1.0 m/s and held together by a string. The spring between them has a spring constant of 140 N/m and is compressed 4.5 cm. The carts slide past a flame that burns through the string holding them together. Afterward, what are the ...

### Physics

A cart of mass m1 = 12 kg slides down a frictionless ramp and is made to collide with a second cart of mass m2 = 19 kg, which then heads into a vertical loop of radius 0.23 m. Determine the height h from which cart 1 would need to start to make sure that cart 2 completes the ...

### physics

Two carts of masses m and 3m are at rest on a horizontal frictionless track. A person pushes each cart with the same force F for 5 s. If the kinetic energy of the lighter cart after the push is K = 180J, the kinetic energy of the heavier cart is :

### Physics

I know I said I didn't know how to start my last question and them figured it out on my own but this one I have tried to work out and really can't get. We have two carts that have magnets to keep them from touching. One cart is initially at rest and we push the second cart ...

### Physics

A dynamics cart with a friction pad is placed at the top of an inclined track and released from rest. The cart accelerates down the incline at a rate of .60m/s^2. If the track is angled at 10 degrees above the horizontal, determine the coefficient of kinetic friction between ...

### physics

A 1.o kg cart A and 2.0 kg cart B are at rest on a frictionless table. A cord and a spring of negligible mass join the two carts. The spring is compressed 0.060m between the two carts until the spring's potential energy is 12 Joules. When the cord is cut, the spring will force...

### Physics please help!

I have tried to work this one out and really can't get it. We have two carts that have magnets to keep them from touching. One cart is initially at rest and we push the second cart towards it. Because the two carts will not actually touch, the collision is elastic. Use the ...

### physics

Jennifer (mass 58.0 kg) is standing at the left end of a 13.0 m long 594.0 kg cart that has frictionless wheels and rolls on a frictionless track. Initially both Jennifer and the cart are at rest. Suddenly, Jennifer starts running along the cart at a speed of 5.70 m/s relative...

### Physics

A cart of apples is rolling toward you in the street. It’s velocity is 2m/s. Its total mass is 50kg. You are running toward the cart of apples (hint your velocity is opposite direction of the carts velocity). You have a mass of 45kg. What velocity must you be running at to ...

### Physics

The following figure represents the ride for a cart with a mass of 200 kg along a frictionless track. a. Calculate the velocity of the cart at points A, B, and C if the cart is dropped from a height of 100m with a initial velocity of 10 m/s. b. Calculate the height of the ...

### Physics

A baggage cart full of luggage is coasting at a speed vA across the airport taxiway. When eighteen percent of the mass of the cart and luggage is thrown off the cart, parallel to the ground and in the forward direction, the cart is brought to a halt. If the direction in which ...

### please help physics!!!!

Two dynamics carts are placed end to end. Cart 1 (1.2 kg) is stuck to cart 2 (1.8 kg). Cart 1 is pushed with a force of 18.9 N (west),causing cart 1 to push cart 2 forward. Ignore the force of friction. Calculate the acceleration of each cart Calculate the force that cart 1 ...

### physics

two air carts of mass m1=0.84kg and m2=0.42kg are placed on a frictionless track. cart1 is at rest and has a spring bumper of constant force F=690N/m.cart2 has a metal bumper and moves towards cart1 with a speed V=0.68m/s. A) what is the speed of the two carts at the momentum ...

### Physics

Cart A, of mass 3.00 kg, approaches and collides with cart B, which has a mass of 7.00 kg and is initially at rest. When the springs have reached their maximum compression, a. cart A has come to rest relative to the ground. b. both carts have the same velocity. c. both carts ...

### Physics

Cart A, of mass 3.00 kg, approaches and collides with cart B, which has a mass of 7.00 kg and is initially at rest. When the springs have reached their maximum compression, a. cart A has come to rest relative to the ground. b. both carts have the same velocity. c. both carts ...

### science

On a frictionless air track, cart A hits cart B moving at a velocity of 2 miles per second to the right. Which answer predicts what will happen?

### physics please help

suppose a cart of mass m = 969 g is initial moving at speed v0 = 5.17 m/s. It strikes a spring attached to a fixed wall, comes to a stop, and bounces back at speed vf = 4.48 m/s. Assume the track is frictionless. a) Find the magnitude of the impulse exerted by the spring on ...

### maths,science, physics

A small cart of mass 300g when emty can move freely on a horizontal surface. The cart contains 100g of sand and moves initially with speed of 18cm s^-1. a)what would be the speed of the cart if a further 200g of sand were dropped vertically into it from a stationary container...

### Physics

Am I correct? Two carts have a compressed spring between them and are initially at rest. One of the carts has total mass, including its contents, of 5.0 kg, and the other has total mass of 3.0 kg. If the 3.0 kg cart is moving at 3.0 m/s after the spring is allowed to push the ...

### Physics

A low friction cart (similar to what you use in the lab) collides with a second low friction cart. Cart A has a mass of 0.500 kg and cart B has a mass of 0.750 kg. Glider A was moving at 40.0 cm/s before the collision. Glider B was at rest. (a) The carts have velcro on them so...

### physics

A 14.0 kg cart is moving with a velocity of 7.25 m/s down a level hallway. A constant force of -10.0 N acts on the cart, and its velocity becomes 3.20 m/s. Assume that air resistance is negligible. (a) What is the change in kinetic energy of the cart? (b) How much work was ...

### physics

A cart with a mass is of 6 kg rolls across a level surface. The wheels on the cart make the effects of friction negligible. A force of 3.0 N is applied to the cart, describe the carts motion.

### physics

A 10 kg cart was observed moving north with a speed of 15 m/s before it collided with an identical cart at rest. The collision was observed to cause the carts to couple and move together as one. What is in Joules the kinetic energy of the system of both carts after the collision?

### PHYSICS

A roller coaster powered by a spring launcher follows a frictionless track as shown below. The roller coaster cart has a mass of 500 kg, and the spring launcher has a spring constant of 1500 N/m. d. What is the fastest speed the cart reaches anywhere on the track?

### physics

A constant force is exerted for a short time interval on a cart that is initially at rest on an air track. This force gives the cart a certain final speed. Suppose we repeat the experiment but, instead of starting from rest, the cart is already moving with constant speed in ...

### physics help

1. A roller coaster car starts from rest and rolls down a frictionless track, reaching speed fv at the bottom. a. If you want the car to go two times as fast at the bottom, by what factor must you increase the height of the track? b. Does your answer to part (a) depend on ...

### Physics

I think I chose the correct answer. In a closed system, two carts have a compressed spring between them. One of the carts has a total mass, including its contents, of 2.0 kg, and the other has total mass of 1.0 kg. Which cart experiences the momentum change of greater ...

### Physics

In procedure 1: suppose the hanging mass is mH = 203 g and the mass of the cart is mC = 1286 g. a) Assume there is no friction anywhere in the system, and the system starts at rest. i. Find the magnitude of the acceleration of the masses. a = m/s2 ii. Find the magnitude of the...

### physics

A 1.0-kg cart and a 0.50-kg cart sit at different positions on a low-friction track. You push on the 1.0-kg cart with a constant 2.5-N force for 0.15m . You then remove your hand, and the cart slides 0.35 m and strikes the 0.50-kg cart. By what amount does your force change ...

### physics

7. A cart like the one we use in lab accelerates down a 20° incline (and since the wheels are smooth, ignore friction for now). Break the force of gravity into components (leave mass as m for now), find the cart’s acceleration, and determine how long it should take the cart...

### Physics

A cart is launched on an air track with a certain speed from the force of a compressed spring. If you wanted to launch the cart at twice the speed, the spring should be compressed by? I say twice as much.

### physics

Two Carts have a perfectly inelastic collision. Cart A has mass 47.2 kg and velocity 6.33 m/s directed north immediately before the collision. Cart B has mass 41.1 kg and velocity 4.4 m/s directed west immediately before the collision. What is the speed of the two carts, stuck...

### Physics

3. A low friction cart (similar to what you use in the lab) collides with a second low friction cart. Cart A has a mass of 0.500 kg and cart B has a mass of 0.750 kg. Glider A was moving at 40.0 cm/s before the collision. Glider B was at rest. (a) The carts have velcro on them...

### Physics

A shopper in a supermarket pushes a loaded 32 kg cart with a horizontal force of 12 N. How far will the cart move in 3.5 s if the shopper places an 85 N child in the cart before pushing? I don't know how I can add the 85 N to the 32 kg or if I can or how that works in an ...

### physics

jabu phuses a cart that is of mass 5kg with a speed of 1m,s she suddenly increase the force acting on the cart to move 2m,s for a distance of 50m (a)calculate the force causing the cart to speed up

### physics

A small, 250\g cart is moving at 1.50m/s on a frictionless track when it collides with a larger, 4.00kg cart at rest. After the collision, the small cart recoils at 0.890m/s . What is the speed of the large cart after the collision?

### Physics

A constant force is exerted for a short time interval on a cart that is initially at rest on an air track. This force gives the cart a certain final speed. Suppose we repeat the experiment but, instead of starting from rest, the cart is already moving with constant speed in ...

### Physics

Two carts with masses of 4.24 kg and 3.44 kg move toward each other on a frictionless track with speeds of 4.90 m/s and 3.51 m/s respectively. The carts stick together after colliding head-on. Find the final speed.

### Physicss....

Two carts with masses of 4.24 kg and 2.22 kg move toward each other on a frictionless track with speeds of 4.55 m/s and 3.16 m/s respectively. The carts stick together after colliding head-on. Find the final speed.

### physics

Two carts with masses of 4.00 kg and 3.40 kg move toward each other on a frictionless track with speeds of 4.70 m/s and 3.56 m/s respectively. The carts stick together after colliding head-on. Find the final speed.