What is the velocity of the combined wreck, assuming a completely inelastic collision?

Question

A car (mass = 1500kg) and a small truck (mass = 2000kg) collide at right angles at an icy intersection. The car was traveling east at 20 m/s and the truck was traveling north at 20m/s when the collision took place.

Answer 1

Lets consider the eastward direction to be the i-direction, and

the northward° direction to be the j-direction.

Let

m = 1500 kg be the mass of the car,

M = 2000 kg be the mass of the truck,

v = 20i m/s be the velocity of the car,

V = 20j m/s be the velocity of the truck,

w be the velocity of the combined wreck (to be calculated).

By conservation of momentum

(m+M)w = mv + MV

w = (m/(m+M))v + (M/(m+M))V

Substituting actual values

w = (1500/3500)20i + (2000/3500)20j = 60i/7 + 80j/7

The angle of the resulting velocity vector is

arctan(80/60) = 53.13° from the eastward direction.

The speed of the wreck is

√((60/7)² + (80/7)²) = 100/7 = 14.3 m/s