Question

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1500 kg and is approaching at 9.5 m/s due south. The second car has a mass of 750 kg and is approaching at 17 m/s due west.

A) Calculate the magnitude of the final velocity, in meters per second, of the cars.

B) Calculate the direction of the final velocity, in degrees, south of west of the cars.

C) What's the change in kinetic energy, in joules, for the collison? (This energy goes into deformation of the cars)

Answer 1

from law of conservation of momentum

m1v1(-j) + m2v2(-i) = (m1 + m2)v

v = [m1v1 / (m1 + m2)](-j) + [m2v2 / (m1 + m2)](-i)

v = [1500*9.5 / (1500 + 750](-j) + [750*17 / (1500 + 750)](-i)

v = 6.33(-j) + 5.67(-i)

manitude of the velocity is

v = sqrt(6.33^2 + 5.67^2)

v = 8.56 m/s

b)

theta = tan^-1(vy/vx)

theta = tan^-1(6.33/5.67)

theta = 48 degree. south to west

c)

The lost in kinetic energy is

KE = KEf - KEi

KE = 1/2m1v1^2 + 1/2m2v2^2 - 1/2(m1 + m2)v^2

KE = 1/2[1500*9.5^2 + 750*17^2 - (1500 + 750)8.56^2]

KE = 187259.4 J