Question

A car of mass 1200. kg, moving with a speed of 72.0 mph on a highway, passes a small SUV with a mass 1 times bigger, moving at 2/3 the speed of the car. a) What is the ratio of the momentum of the SUV to that of the car? b) What is the ratio of the kinetic energy of the SUV to that of the car? Please show all work!

Answer 1

let m1 = 1200 kg

u1 = 72 mph

1 mph = 0.447 m/s

then

u1 = 72 mph = 72*0.447 = 32.184 m/s

m2 = 1200 kg

u2 = (2/3)*32.184 = 21.456 m/s

momentum of SUV is p_SUV = m2*u2 = 1200*21.456 = 25747 kgm/s

momentum of car is p_car = m1*u1 = 1200*32.184 = 38620.8 kg m/s

a) p_SUV/p_car = 25747/38620.8 =0.67

b) we know that relation between kinetic energy and momentum is KE = p^2/(2*m)

since mass m is same for SUV and car then

KE_SUV / KE_car = (p_SUV/p_car)^2 = 0.67^2 = 0.45