Question

A 4350 kg truck, driving 7.39 m/s, runs into the back of a stationary car. After the collision, the truck moves 4.55 m/s and the car moves 11.5 m/s, both in the same direction. What is the mass of the car?

Answer 1

1074.26 kg

Step-by-step explanation:

Answer 2

The mass of the car is 1074.26 kg.

Step-by-step explanation:

Let the mass of the car be x.

Given:

Mass of truck,
`M=4350` kg

Initial velocity of truck,
`u_1=7.39` m/s

Initial velocity of car,
`u_2=0` m/s

Final velocity of truck,
`v_1=4.55` m/s

Final velocity of car,
`v_2=11.5` m/s

When two bodies collide with no external force acting on the system, their total momentum remains conserved.

Therefore, initial momentum = final momentum

`Mu_1+x u_2=Mv_1+xv_2\\4350*7.39+0=4350* 4.55+11.5x\\32146.5=19792.5+11.5x\\11.5x=32146.5-19792.5\\11.5x=12354\\x=(12354)/(11.5)=1074.26\textrm{ kg}`

Hence, the mass of the car is 1074.26 kg.