Question

A small car of mass m and initial speed v0 collides hear-on on an icy road with a truck of mass 4m going toward the car with initial speed (1/2)v0. If the coefficient of restitution in the collision is 1/4, find the speed and direction of each vehicle just after colliding.

Answer 1

consider the initial direction of car as positive, and using conservation of momentum, we have

m * v_o - 4m * v_o / 2 = mv1f + 4mv * v2f

m v_o ( 1 - 2) = m ( v1f + 4v2f)

- v_o = v1f + 4v2f ----------- (1)

from equation of coefficient of restituion

1/4 = v2f - v1f / v_o + v_o / 2

0.25 ( v_o + 0.5v_o) = v2f - v1f

0.375v_o = v2f - v1f ----------- (2)

from (1)

v1f = - v_o - 4v2f

put this in (2)

0.375v_o = v2f - ( - v_o - 4v2f )

0.375v_o = v2f + v_o + 4v2f

-0.625v_o = 5v2f

v2f = - 0.125v_o m/s (final speed of truck)

and

v1f = - v_o - ( 4 * - 0.125v_o)

v1f = - v_o + 0.5v_o

v1f = - 0.5v_o m/s ( final speed of car)

as we can see both car and truck are moving in the direction same as initial direction of truck .