Object A has a mass of 40 kg and is travelling at 24 m/s [E] ..

Question

Object A has a mass of 40 kg and is travelling at 24 m/s [E] and object B has a mass of 29 kg and is travelling at 33 m/s [W]. After these two objects collide, object B has a velocity of 16.8 m/s [E]. Determine the velocity of object A after the collision.

Answer 1

Solution:

This is a conservation of momentum problem that is Pi is momentum before collision is equal to Pf or momentum after collision Pi = Pf

Pi = m1V1 + m2V2 = Pf = m1 V1' + m2 V2'

Given:

m1 = mass of object A = 40 kg

V1 = velocity of object A before collision= +24 m/s ( + ve direction east)

m2 = mass of object B = 29 kg

V2 = velocity of object B before collision = -33 m/s ( -ve direction west)

V2' = velocity of object B after collision = + 16.8 m/s ( +ve direction east)

Required:

V1' = ? , velocity of object A after collision

Substitute values in the above equation, ( 40kg)(24m/s) + (29kg)(-33m/s) = (40 kg)(V1')+(29kg)(16.8 m/s)

solving, 960 kg.m/s -957 kg.m/s = 40 kg V1' + 487.2 kg.m/s, 3 kg.m/s = 40 kg V1' + 487.2 kg.m/s

3 kg.m/s - 487.2 kg.m/s = 40 kg V1'

-484.2 kg.m/s = 40 kg V1' , and V1' = ( -484.2 kg.m/s / 40 kg) = -12.1 m/s ( -ve sign indicates that object A is moving west)