A railway truck traveling along a level track at 9 m/s collides with, and becomes coupled to, a stationary truck. Find the velocity of the coupled trucks immediately after the collision if the stationary truck has a mass which:
a. equal to the mass of the moving truck
b. twice the mass of the moving truck
a. Velocity of coupled truck will be half of the velocity of moving truck
b. Velocity of coupled truck will be 1/3rd of the velocity of moving truck
This topic is about collisions, and this type of collision is perfectly inelastic collision, and the formula for this is
m_{a }v_{a }+ m_{b }v_{b} = ( m_{a }+ m_{b}) v' ---> remember that we have only 1 velocity after they collide.
If we assume the mass of the moving truck is 1000 kg , then substitute all the given values and using the formula given above, we have
v' = m_{a} v_{a }+ m_{b }v_{b } / m_{a }+ m_{b}
v' = 1000kg (90m/s) + 1000kg(0m/s) / 1000kg + 1000kg
v' = 9000 kg m/s + 0 kg m/s / 2000kg
v' = 4.5 m/s ---> this is your answer in letter A if the mass of the moving truck and stationary truck are the same.
But in letter B since the mass of the stationary truck is doubled, here's the solution
v' = 1000kg (90m/s) + 2000kg (0m/s) / 1000kg + 2000kg
v' = 9000 kg m/s + 0 kg m/s = 3000kg
v' = 3 m/s ----> this is your answer in letter B