16-g mass is moving in the +x direction at 30 cm/s while a 4-g mass is moving in the -x direction at 50 cm/s. they collide head on and stick together. find their velocity after the collision.

see above

-16

To find the velocity of the two masses after the collision, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.

The momentum of an object can be calculated by multiplying its mass (m) by its velocity (v). The formula for momentum is:

Momentum (p) = mass (m) × velocity (v)

Before the collision, the momentum of the 16-g mass moving in the +x direction is:
p1 = (16 g) × (30 cm/s)

Before the collision, the momentum of the 4-g mass moving in the -x direction is:
p2 = (4 g) × (-50 cm/s)

Since the masses stick together after the collision, their total mass is the sum of the individual masses, which is 16 g + 4 g = 20 g.

Now, using the conservation of momentum principle, we can equate the initial momentum to the final momentum:

p1 + p2 = pf

Where pf is the final momentum. Using the above values, we have:

(16 g) × (30 cm/s) + (4 g) × (-50 cm/s) = (20 g) × (vf)

Simplifying this equation gives:

(480 g*cm/s - 200 g*cm/s) = (20 g) × (vf)

(280 g*cm/s) = (20 g) × (vf)

To find the velocity (vf), we need to convert the units to a consistent form, such as kg and m/s. Converting grams (g) to kilograms (kg) is done by dividing by 1000, and converting centimeters (cm) to meters (m) is done by dividing by 100.

(280 g*cm/s) = (0.28 kg*m/s) = (20 g) × (vf)

Now, we can solve for vf:

(0.28 kg*m/s) = (20 g) × (vf)

vf = (0.28 kg*m/s) / (20 g)

vf ≈ 0.014 m/s

Therefore, the velocity of the two masses after the collision is approximately 0.014 m/s in the direction of the initial 16-g mass (+x direction).