Question

A car with mass 1500 kg traveling east at 25 m/s collides at an intersection with a 2500kg van traveling north at a speed of 20 m/s. Find the magnitude and direction of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision and assuming no friction.

Answer 1

here,

the mass of car , m1 = 1500 kg

initial velocity of 1 , u1 = 25 m/s i

the mass of Van , m2 = 2500 kg

initial velocity of 2 , u2 = 20 m/s j

let the final velocity of wreckage be v

using conservation of momentum

m1 *u1 + m2 * u2 = ( m1 + m2) * v

1500 * 25 i + 2500 * 20 j = (1500 + 2500) * v

v = 9.375 i m/s + 12.5 j m/s

the magnitude of velocity of wreckage , |v| = sqrt(9.375^2 + 12.5^2) = 15.6 m/s

the direction of velocity , theta = arctan(12.5 /9.375)

theta = 53.13 degree North of East