Question

A body of mass 20kg moving with a velocity of 80m/s collides with another body of mass 50kg and moving with velocity of 50 m/s in opposite direction.If they move together after collision find their common velocity

Answer 1

Mass of first object (m1) = 20 kg
velocity (v1) = 80 m/s

Mass of second object (m2) = 50 kg
velocity (v2) = -50 m/s
(minus sign is due to motion in opposite direction)

After collision, they move together.
total mass, M = 20+50 = 70kg
Let the final velocity = V

According to conversation of momentum:

total initial momentum = total final momentum

=> m1v1 + m2v2 = MV

=> 20×80 + 50×(-50) = 70×V

=> 1600 - 2500 = 70V

=> -900 = 70V

=> V = -900/70

=> V = -12.86 m/s

Their common velocity is 12.86 m/s in the direction of motion of the 50 kg body.

Answer 2

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Mass of first object (m1) = 20 kg

velocity (v1) = 80 m/s

Mass of second object (m2) = 50 kg

velocity (v2) = -50 m/s

(minus sign is due to motion in opposite direction)

After collision, they move together.

total mass, M = 20+50 = 70kg

Let the final velocity = V

According to conversation of momentum:

total initial momentum = total final momentum

=> m1v1 + m2v2 = MV

=> 20×80 + 50×(-50) = 70×V

=> 1600 - 2500 = 70V

=> -900 = 70V

=> V = -900/70

=> V = -12.86 m/s

Their common velocity is 12.86 m/s in the direction of motion of the 50 kg body.