# A uniform solid ball rolls smoothly along a floor, then up a ramp at 13.0°. It momentarily stops when it has rolled 1.30 m along the ramp. What was its initial speed?

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**Physics**

A uniform solid ball rolls smoothly along a floor, then up a ramp inclined at 13.5 degrees. It momentarily stops when it has rolled 1.65 m along the ramp. What was its initial speed?

**Physics**

A crate full of artichokes rests on a ramp that is inclined 10.0° above the horizontal. Give the direction of the normal force and the friction force acting on the crate in each of these situations. (a) The crate is at rest. Normal Force : 1.perpendicular to and away from the...

**Physics**

A crate full of artichokes rests on a ramp that is inclined 10.0° above the horizontal. Give the direction of the normal force and the friction force acting on the crate in each of these situations. (a) The crate is at rest. Normal Force : 1.perpendicular to and away from the...

**Physics**

A crate full of artichokes rests on a ramp that is inclined 10.0° above the horizontal. Give the direction of the normal force and the friction force acting on the crate in each of these situations. (a) The crate is at rest. Normal Force : 1.perpendicular to and away from the...

**Physics**

A uniform solid sphere of mass M and radius R is rolling without sliding along a level plane with a speed v = 2.70 m/s when it encounters a ramp that is at an angle è = 20.4° above the horizontal. Find the maximum distance that the sphere travels up the ramp if the ramp is ...

**physics**

A uniform solid sphere of mass M and radius R is rolling without sliding along a level plane with a speed v = 2.30 m/s when it encounters a ramp that is at an angle è = 27.6° above the horizontal. Find the maximum distance that the sphere travels up the ramp if the ramp is ...

**Physics**

A block is placed on a frictionless ramp at a height of 14.5 m above the ground. Starting from rest, the block slides down the ramp. At the bottom of the ramp, the block slides onto a frictionless horizontal track without slowing down.At the end of the horizontal track, the ...

**physics**

A solid sphere is released from the top of a ramp that is at a height h1 = 1.95 m. It goes down the ramp, the bottom of which is at a height of h2 = 1.38 m above the floor. The edge of the ramp is a short horizontal section from which the ball leaves to land on the floor. The ...

**physics**

Where did the waste energy go to? A ball rolls off the ramp on the edge of a table heading downward and hits the ground. Was the energy lost or gained a direct relation to the distance that the metal ball travelled along the ramp?

**physics**

A ball rolls up a ramp and then back down again. The ramp is oriented so that the ball is rolling to the right as it rolls up the ramp. Assume that positive v and a vectors point to the right. Which statement is true about the ball's horizontal acceleration?

**physics**

I am having great difficulty with this question. A block is placed on a frictionless ramp at a height of 12.5 m above the ground. Starting from rest, the block slides down the ramp. At the bottom of the ramp, the block slides onto a frictionless horizontal track without ...

**physics**

A ball rolls up a ramp which abruptly ends with the ramp dropping straight down. The ball launches off the end of the ramp while still traveling at an upward trajectory, goes through projectile motion, and returns to the same height as the base of the ramp. Ignoring any ...

**physics**

a 5.4 kg ball slides along a friction-less, horizontal surface at 6.2 m/s. The ball then encounters a ramp which slopes upward. The ball slides up the ramp, slowing down until it stops and slides back down. what is the kinetic energy of the ball as it slides along the friction...

**physics**

A ball rolls up a ramp and then back down again. The ramp is oriented so that the ball is rolling to the right as it rolls up the ramp. Assume that positive v and a vectors point to the right. Which statement is true about the ball's horizontal acceleration? b. The ball has a ...

**physics**

A skateboard with mass M rolls down a ramp, starting from rest. It takes time T to roll a distance L along the ramp. In terms of M, T, and L, what is the skateboard’s acceleration down the ramp?

**physics**

A ball is rolled up a ramp at 2.50 m/s. The ball slows down for 5.00 s and then rolls back down. Assume frictions isn't a factor and that the up ramp is the positive. At what point does the ball's acceleration change and what is the acceleration on the way down?

**physics**

A solid, uniform disk of radius 0.250 m and mass 60.4 kg rolls down a ramp of length 4.60 m that makes an angle of 18.0° with the horizontal. The disk starts from rest from the top of the ramp. (a) Find the speed of the disk's center of mass when it reaches the bottom of the ...

**Ap physics**

A ball rolls down an incline with an acceleration of 10 cm/s^2. If it starts with an initial velocity of 0 cm/s and has a velocy of 50 cm/s when it reaches the bottom of the ramp, how long is the ramp?

**PHYSICS (please help)**

A solid, uniform disk of radius 0.250 m and mass 51.1 kg rolls down a ramp of length 4.60 m that makes an angle of 18° with the horizontal. The disk starts from rest from the top of the ramp. a)Find the speed of the disk's center of mass when it reaches the bottom of the ramp...

**Physics and Math**

A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp, which is at an angle 3o Degree above the horizon. A linear spring, whose length is not negligible, is attached to the bottom of the ramp. The ball is released from a distance of 1 m above the spring...

**Math**

Amanda wants to shorten the wheelchair ramp at her front door. The current ramp is 13 feet along the horizontal and the step is 9 inches high. If she doubles the measure of the angle that the ramp makes with the walkway, how long will the new ramp be to the nearest inch?

**Physics**

A box of mass 1.50 kg is given an initial velocity of 12.5 m/s up an inclined ramp that makes an angle of 25.0o with the ground, which is horizontal. The coefficient of kinetic friction between the box and the ramp is 0.240. How long does the box slide up the ramp before it ...

**Physics**

A box of mass 1.50 kg is given an initial velocity of 12.5 m/s up an inclined ramp that makes an angle of 25.0o with the ground, which is horizontal. The coefficient of kinetic friction between the box and the ramp is 0.240. How long does the box slide up the ramp before it ...

**Physics**

A solid sphere, a hoop, and a solid disk. all with equal masses and radii, roll at the same translational speed along a horizontal surface toward a ramp inclined at a 30 degree angle. Which of the three will make it furthest up the ramp before it stops and begins to roll back ...

**Physics**

A 10 kg box is held 2 meters up a ramp that is inclined at 35 degrees. It is released frpm rest, slides down the ramp and across the floor. the coefficient of friction is 0.15. How far along the floor will the box slide?

**physics**

a 65 kg bag is dragged along a 12m ramp in order to get from the ground to the floor of the loading dock 2m above the ground. determine the efficiency of of the ramp. The frictional force acting on the bag is 50N due to the ramp. I don't understand how to the find the energy ...

**physics please help**

a 65 kg bag is dragged along a 12m ramp in order to get from the ground to the floor of the loading dock 2m above the ground. determine the efficiency of of the ramp. The frictional force acting on the bag is 50N due to the ramp. I don't understand how to the find the energy ...

**Physics**

A child's game consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. By compressing the spring, the child can launch the ball up the ramp. The spring has a spring constant k, the ball has a mass m, and ...

**physics**

A ramp causes a ball to accelerate at - 4 m/s the ball is rolled up the ramp at 13 m/s find the ball velocity after rolling for 6 seconds you must show your work

**frictionless ramp**

Suppose a 19.3 kg curling stone was on a frictionless ramp. If the ramp is 4.76 m tall and 19.5 m long (along the incline), how much mass must hang from the pulley in order that the stone not accelerate up or down the ramp?

**Physics**

After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of v = 3.41 m/s To reach the rack, the ball rolls up a ramp that rises through a vertical distance of h = 0.529 m. What is the linear speed of the ball when it ...

**physics**

After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of v = 3.27 m/s To reach the rack, the ball rolls up a ramp that rises through a vertical distance of h = 0.572 m. What is the linear speed of the ball when it ...

**Physics**

After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of = 3.18 m/s. To reach the rack, the ball rolls up a ramp that rises through a vertical distance of = 0.510 m. What is the linear speed of the ball when it ...

**Physics**

A semitrailer is coasting downhill along a mountain highway when its brakes fail. The driver pulls onto a runaway-truck ramp that is inclined at an angle of 10.0° above the horizontal. The semitrailer coasts to a stop after traveling 137 m along the ramp. What was the truck's...

**Physics**

A box weighing 8.0 kg has to be moved from the floor to the back of the truck, using a ramp 2.5 m long inclined at 30°. The worker gives the box a push so that it has initial velocity of 5.0 m/s. Unfortunately, the friction is more than he estimated and the box stops 1.6 m up...

**Physics**

A ball is rolled up a ramp from the point B shown below, with an initial speed of 5 miles per hour. It continues up the ramp to point C before it begins to roll back down. Throughout the motion up and down the ramp, the ball maintains a constant acceleration (this is always ...

**Physics**

A ball is rolled up a ramp with an initial velocity of +10m/s. It arrives at the bottom of the ramp with the same speed 5 seconds later. What is the ball acceleration for the whole trip? What is the velocity after 2 seconds? After 3 seconds?

**physics**

how does increasing the height of a ramp affect how far a ball rolls down the ramp?

**physics**

a 65 kg bag is dragged along a 12m ramp in order to get from the ground to the floor of the loading dock 2m above the ground. determine the efficiency of of the ramp. I don't understand how to the find the energy output and input.

**physics**

A semi-trailer is coasting downhill along a mountain highway when its brakes fail. The driver pulls onto a runaway truck ramp that is inclined at an angle of 17.0° above the horizontal. The semi-trailer coasts to a stop after traveling 110 m along the ramp. What was the truck...

**physics**

A semi-trailer is coasting downhill along a mountain highway when its brakes fail. The driver pulls onto a runaway truck ramp that is inclined at an angle of 19.0° above the horizontal. The semi-trailer coasts to a stop after traveling 170 m along the ramp. What was the truck...

**physics**

A semi-trailer is coasting downhill along a mountain highway when its brakes fail. The driver pulls onto a runaway truck ramp that is inclined at an angle of 13.0° above the horizontal. The semi-trailer coasts to a stop after traveling 190 m along the ramp. What was the truck...

**PHYSICS**

A mass on a frictinless inclined ramp is connected to a rope with tension T. Complete the senteces with correct selection: -increases -decreases -stays the same a) If the block is moving up the ramp and theta=30 deg, its speed initally _________ if T=(mg)/2 b) If the block is ...

**general physics**

A semi-trailer is coasting downhill along a mountain highway when its brakes fail. The driver pulls onto a runaway truck ramp that is inclined at an angle of 13.0° above the horizontal. The semi-trailer coasts to a stop after traveling 190 m along the ramp. What was the truck...

**Physics**

The builders of the pyramids used a long ramp to lift 21000-kg (21-ton) blocks. If a block rose 0.86 m in height while traveling 20 m along the ramp’s surface, how much uphill force was needed to push it up the ramp at constant velocity?

**physics**

The builders of the pyramids used a long ramp to lift 21000-kg (21-ton) blocks. If a block rose 1.0 m in height while traveling 21 m along the ramp’s surface, how much uphill force was needed to push it up the ramp at constant velocity?

**Phy**

A 2.0 kg ball is placed against a spring of force constant 750N/m, which has been compressed 0.28m. The spring is released and the ball moves along a horizontal frictionless surface and up a ramp. Calculate the... a) maximum elastic potential energy of the spring (could it be ...

**Scientific Method**

Joe Student rolled a toy car down a ramp and measured how far it traveled along the floor. He recorded the distance along with the original mass of the toy car. Then, he taped a penny to the roof of the same toy car, measured its new mass, and rolled it down the same ramp from...

**physics**

A 50kg barrel of Bud is rolled up a 10 meter ramp to the back of the truck.The ramp makes a 30degree angle with the ground. What is the potential energy of the barrel at the top of the ramp? How uch work was done against gravity to get it to the top of the ramp?

**physics**

A dude is spinning a 1.0 kg mass on the end of a 1.5 meter string. He gets it spinning at a constant rate of 4.0 rev/sec. The string breaks such that the mass is thrown into projectile motion with an initial angle of 45° to the ground (assume that it is launched from ground ...

**college physics**

The builders of the pyramids used a long ramp to lift 21000-kg (21-ton) blocks. If a block rose 1.1 m in height while traveling 20 m along the ramp’s surface, how much uphill force was needed to push it up the ramp at constant velocity?

**science**

Identify the test (independent) variable, the outcome (dependent) variable, at least 3 controlled variables, and the error Joe made in the following experiment: Joe Student rolled a toy car down a ramp and measured how far it traveled along the floor. He recorded the distance ...

**physics**

A box of mass 5.0 kg starting from rest slides down a 1.8 m long ramp inclined at an angle of 22.0 deg. from the horizontal. If the ramp is frictionless, how long will it take the box, starting from rest, to reach the bottom of the ramp? if the frictionless ramp is replaced ...

**General Physics**

A 4 kg block slides along a frictionless horizontal with a speed of 5.1 m/s. After sliding a distance of 7 m, the block makes a smooth transition to a frictionless ramp inclined at an angle of 13 degrees to the horizontal. The acceleration of gravity is 9.81 m/s2. How far up ...

**Physics**

Consider the gravitational potential, kinetic, and total mechanical energies of a cart moving down an inclined ramp. (Also, let gravitational potential energy be defined to be zero when the cart is at the bottom of the ramp. A. Write an expression for the gravitational ...

**PHYSICS!!**

A person thought it would be a good idea to change a tire on the side of a hill. The tire has a width of W = 0.30 m and a radius of R = 0.40 m. The inside of the wheel is empty, but the wheel is solid from a radius of R/2 to R with uniform density. The density of the material ...

**Physics**

A luggage handler pulls a 20kg suitcase up a ramp inclined at 25 degrees above the horizontal by a force F of magnigutde 145N that acts parallel to the ramp. The coefficient of kinetic friction between the ramp and the incline is .30. If the suitcase travels 4.6 m along the ...

**Physics**

Eddie the Eagle, British Olympic ski jumper, is attempting his most mediocre jump yet. After leaving the end of the ski ramp, he lands downhill at a point that is displaced 62.2 m horizontally from the edge of the ramp. His velocity just before landing is 29.0 m/s and points ...

**prealgebra**

A barrel shaped like a cylinder is laid on its side and rolled up a ramp. The barrel has a circular base that is 0.9m in diameter. If the barrel turns 37 times in being rolled up the ramp, how long is the ramp? Use the value 3.14 for π . Round your answer to the nearest ...

**Physics**

Starting from rest, a 11.50 kg suitcase slides 3.18 m down a frictionless ramp inclined at 40° from the floor. The suitcase then slides an additional 5.22 m along the floor before coming to a stop. (a) Determine the suitcase's speed at the bottom of the ramp. (b) Determine ...

**physics**

Starting from rest, a 11.70 kg suitcase slides 3.14 m down a frictionless ramp inclined at 40° from the floor. The suitcase then slides an additional 4.68 m along the floor before coming to a stop. (a) Determine the suitcase's speed at the bottom of the ramp. (b) Determine ...

**Physics**

You roll a 5 kg bowling ball (R=20cm) with an initial speed of 10 m/s up a 30 degree ramp that is 12 m long. Will the ball reach the top of the ramp? (support your answer)

**physics**

A ball rolls along flat ground at 7.0 m/s then encounters a hill. If the ball rolls 15 m up the hill before coming to a stop, what was the acceleration (in m/s2) experienced by the ball as it rolled up the hill?

**Physics**

A 1.20kg ball is rolled down a frictionless ramp whose top is 0.80m above a horizontal spring with ks = 800N/m. The ball reaches the horizontal just in front of the spring. a.) What is the kinetic energy of the ball just before it contacts the spring? b.) What is the velocity ...

**physics**

A ball of radius 0.211 m rolls along a horizontal table top with a constant linear speed of 3.41 m/s. The ball rolls off the edge and falls a vertical distance of 2.27 m before hitting the floor. What is the angular displacement of the ball while the ball is in the air?

**Physics**

15. A refrigerator weighing 1500 N is to be lifted onto a truck bed that is 1.0 m above the ground. When pushed up a slanting ramp 2.0 m in length a force parallel to the ramp of only 800 N is required to move it at constant velocity. Comparing the work involved in lifting the...

**physics**

Starting from rest, a 10.7 kg block slides 2.60 m down to the bottom of a frictionless ramp inclined 30.0° from the floor. The block then slides an additional 4.70 m along the floor before coming to a stop. (a) Determine the speed of the block at the bottom of the ramp. m/s (...

**physics**

An 70.0 N box of clothes is pulled 24.0 m up a 30.0° ramp by a force of 115 N that points along the ramp. If the coefficient of kinetic friction between the box and ramp is 0.22, calculate the change in the box's kinetic energy.

**Physics**

An 52.0 N box of clothes is pulled 7.3 m up a 30.0° ramp by a force of 103 N that points along the ramp. If the coefficient of kinetic friction between the box and the ramp is 0.22, calculate the change in the box's kinetic energy.

**Physics**

An 52.0 N box of clothes is pulled 7.3 m up a 30.0° ramp by a force of 103 N that points along the ramp. If the coefficient of kinetic friction between the box and the ramp is 0.22, calculate the change in the box's kinetic energy.

**physics**

An 66.0 N box of clothes is pulled 5.5 m up a 30.0° ramp by a force of 116 N that points along the ramp. If the coefficient of kinetic friction between the box and the ramp is 0.22, calculate the change in the box's kinetic energy.

**physics**

An 56.0 N box of clothes is pulled 5.2 m up a 30.0° ramp by a force of 104 N that points along the ramp. If the coefficient of kinetic friction between the box and the ramp is 0.22, calculate the change in the box's kinetic energy. J

**physics**

An 56.0 N box of clothes is pulled 5.2 m up a 30.0° ramp by a force of 104 N that points along the ramp. If the coefficient of kinetic friction between the box and the ramp is 0.22, calculate the change in the box's kinetic energy.

**another physics problem that i dont understnad..**

An 58.0 N box of clothes is pulled 5.2 m up a 30.0° ramp by a force of 95 N that points along the ramp. If the coefficient of kinetic friction between the box and the ramp is 0.22, calculate the change in the box's kinetic energy.

**Physics**

A child's toy consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. (Intro 1 figure) The spring has a spring constant k, the ball has a mass m, and the ramp rises a height y above the table, the surface...

**physics**

A ball rolls along a desktop with an uniform velocity of 3 m/s. What is the displacement after 10 seconds have passed? A ball is thrown upward with an initial velocity of 18 m/s? What is the maximum height the ball reaches if the ball is assumed to leave from the ground? &#...

**physics**

A ball rolls along a desktop with an uniform velocity of 3 m/s. What is the displacement after 10 seconds have passed? A ball is thrown upward with an initial velocity of 18 m/s? What is the maximum height the ball reaches if the ball is assumed to leave from the ground? &#...

**Physics**

A solid brass ball of mass 9.5 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 4.2 m, and the ball has radius r << R. (a) What is h if the ball is on the verge of leaving the track when...

**physics**

A box is pushed a distance d along a ramp at a constant speed by a horizontal force, Fa. The mass of the box is m. The ramp is inclined at an angle of above the horizontal and the coecient of kinetic friction between the box and the ramp is k.

**physics : HELP PLEASE**

A ball rolls along a desktop with an uniform velocity of 3 m/s. What is the displacement after 10 seconds have passed? A ball is thrown upward with an initial velocity of 18 m/s? What is the maximum height the ball reaches if the ball is assumed to leave from the ground? &#...

**physics : HELP PLEASE**

A ball rolls along a desktop with an uniform velocity of 3 m/s. What is the displacement after 10 seconds have passed? A ball is thrown upward with an initial velocity of 18 m/s? What is the maximum height the ball reaches if the ball is assumed to leave from the ground? &#...

**Physics**

Suppose the height of the ramp is h1= 0.3 m, and the foot of the ramp is horizontal, and is h2= 1.00 m above the floor. What will be the horizontal distance traveled by the following four objects before they hit the floor? Assume that R= 12.7 mm in each case; assume that the ...

**Physics**

An 82.9 N box of clothes is pulled 28.2 m up a 20.7◦ ramp by a force of 117 N that points along the ramp. The acceleration of gravity is 9.81 m/s^2. If the coefficient of kinetic friction between the box and ramp is 0.29, calculate the change in the box’s kinetic ...

**Physics**

Starting from rest, a 10.0 Kg suitcase slides down a 3.00m long ramp inclined at 30.0 degrees from the floor. The coefficient of friction between the suitcase and ramp is .35. A: what net force is applied to suitcase while it is on the ramp? B: what is the change in the ...

**physics**

Starting from rest, a 10kg suitcase slides down a 3.00m long ramp inclined at 30 degrees from the floor. The coefficient of friction between the suitcase and the ramp is 0.35. 1) what net force is applied to the suitcase while it is on the ramp? 2)what is the change in the ...

**Physics**

A crate of mass 29 kg is pushed up a ramp by a person as shown in the figure below. The person pushes the crate a distance of 25 m as measured along the ramp. Assume the crate moves at constant velocity. Assume the coefficient of kinetic friction between the crate and the ramp...

**physics**

A 5-g marble, released form rest, was allowed to roll on a ramp whose lower end is 25 cm from the floor. When it left the ramp, it behaved like a body in projectile motion. What was the horizontal velocity of this marble when it left the ramp? With what momentum did it leave ...

**physics**

A ball of radius 0.2m rolls along a horizontal table top with a constant linear speed of 3.04 m/s. The ball rolls off the edge and falls a vertical distance of 2.02m before hitting the floor. What is the angular displacement of the ball while it is in the air.

**physics**

An 85.7 N box of clothes is pulled 26.2 m up a 31.7 ◦ ramp by a force of 112 N that points along the ramp. The acceleration of gravity is 9.81 m/s 2 . If the coeﬃcient of kinetic friction between the box and ramp is 0.24, calculate the change in the box’s ...

**Physics**

A uniform, spherical bowling ball of mass m and radius R is projected horizontally along the ﬂoor at an initial velocity v0 = 6.00 m/s. The ball is not rotating initially, so ω0 = 0. It picks up rotation due to (kinetic) friction as it initially slips along the &#...

**physics**

3. In the figure, a runaway truck with failed brakes is moving downgrade at 107 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of θ = 14°. The truck's mass is 1.4 × 104 kg. (a) What minimum length L must the ramp...

**physics**

A hoop is at rest at the top of a 3.0 m long ramp with an angle of evelation of 24°. If the hoop rolls down the ramp, what is the final velocity of the hoop at the bottom of the ramp

**physics**

A 20 kg block slides with an initial speed of 11 m/s up a ramp inclined at an angle of 25o with the horizontal. The coefficient of kinetic friction between the block and the ramp is 0.8. Use energy conservation to find the distance along the incline that the block slides ...

**Science**

A student finds that it takes 0.20s for a ball to pass through phototogates placed 30 cm apart on a level ramp. The end of the ramp is 92 cm above the floor. Where should a coin be placed so tnat the ball strikes it directly on impact with the ground?

**Physics**

A(n) 160 g block is pushed by an external force against a spring with spring constant of 1260 N/m until the spring is compressed by 11.8 cm from its uncompressed length. The compressed spring and block rests at the bottom of an incline of angle θ = 39.0°. Note that the ...

**physics**

A car sits in an entrance ramp to a freeway, waiting for a break in the traffic. The driver sees a small gap between a van and an 18-wheel truck and accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, ...

**physics**

A 2.25 kg ball experiences a net force of 965 N up a ramp. Once the ball reaches the top of the ramp, the force no longer acts. The force acts over a distance of 1.50 m on the ramp. Find the horizontal distance x that the ball travels before it hits the deck. The top of the ...

**Physics**

A crate of mass 40 kg is pushed up a ramp by a person as shown in the figure below. The person pushes the crate a distance of 14 m as measured along the ramp. Assume the crate moves at constant velocity. Assume the coefficient of kinetic friction between the crate and the ramp...

**physics**

In Fig, a runaway truck with failed brakes is moving downgrade at 160 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of è = 11°. The truck's mass is 1.5 x 104 kg. (a) What minimum length L must the ramp have if the ...

**physics**

A small circular object with mass m and radius r has a moment of inertia given by I = cmr2. The object rolls without slipping along the track shown in the figure. The track ends with a ramp of height R = 3.0 m that launches the object vertically. The object starts from a ...