The parking brake on a 2000 kg Cadillac has failed, and it is rolling slowly, at 3.00 mph, toward a group of small children. Seeing the situation, you realize you have just enough time to drive your 2000 kg Volkswagen head-on into the Cadillac and save the children.

With what speed should you impact the Cadillac to bring it to a halt?

1.34112 m/s

Explanation:

From the law of conservation of momentum,

Total momentum before collision = Total momentum after collision

mu+m'u' = V (m+m')

From the question, V = 0 m/s (bring it to halt)

Therefore,

mu+m'u' = 0

Where m = mass of the Cadillac, u = initial velocity of the Cadillac, m' = mass of the Volkswagen, u' = initial velocity of the Volkswagen

make u' the subject of the equation

u' = - mu/m' ... Equation 1

Given: m = 2000 kg, m' = 2000 kg, u = 3.0 mph = (3*0.44704) m/s = 1.34112 m/s

Substitute into equation 1

u' = - 2000 (1.34112) / 2000

u' = - 1.34112 m/s

Hence the speed required to impact the Cadillac to bring it to halt = 1.34112 m/s.