Question

A 1055-kg van, stopped at a traffic light, is hit directly in the rear by a 730-kg car traveling with a velocity of +2.45 m/s. Assume that the transmission of the van is in neutral, the brakes are not being applied, and the collision is elastic. What is the final velocity of each vehicle?

Answer 1

Given that,

m1 = 1055 kg

u1 = 0

m2 = 730 kg

u2 = 2.45 m/s

Let, final final velocities are v1 and v2.

From conservation of momentum,

m1u1 + m2u2 = m1v1 + m2v2 .........(1)

From conservation of energy,

(1/2)m1u1^2 + (1/2)m2u2^2 = (1/2)m1v1^2 + (1/2)m2v2^2 ........(2)

By solving eq (1) and (2),

v1 = (m1 - m2 / m1 + m2)*u1 + (2m1 / m1 + m2)*u2

Since u1 = 0,

v1 = (2m1 / m1 + m2)*u2

v1 = (2*1055 / 1055 + 730)*2.45

v1 = 2.896 m/s

v2 =  (m2 - m1 / m1 + m2)*u2 + (2m1 / m1 + m2)*u1

Since, u1 = 0

v2 = (m2 - m1 / m1 + m2)*u2

v2 = (730 - 1055 / 1055+730)*2.45

v2 = -0.446 m/s