Question

In a road accident, a van of mass 1500 kg moving at a speed of 28m * s ^ - 1 ran into the back of a car of mass 900 kg moving in the same direction at a speed of 11m * s ^ - 1 . As a result of the impact, the car was pushed forward at a speed of 18m * s ^ - 1 .

a Calculate the velocity of the van immediately after the impact.

b Calculate:

i the loss of kinetic energy of the van, ii the gain of kinetic energy of the car,

iii the total change of kinetic energy of the two vehicles.

Answer 1

a. By conservation of momentum:

$$mv+MV=mu+MU,\\\space\\ U=\dfrac{mv+MV-mu}{M}=23.4\text{ m/s}.$$

b i. The loss of kinetic energy of the van:

$$\Delta KE_v=\dfrac12M(U^2-V^2)=177330\text{ J}.$$

b. ii. The gain of kinetic energy of the car:

$$\Delta KE_c=\dfrac12m(u^2-u^2)=91350\text{ J}.$$

b. iii. The total change of kinetic energy of the two vehicles:

$$\Delta KE_c=\Delta KE_v+\Delta KE_c=-268680\text{ J}.$$