With what speed should you impact the 1700kg Cadillac to bring it to a halt?

The parking brake on a 1700 kg Cadillac has failed, and it is rolling slowly, at 1 mph, toward a group of small children. Seeing the situation, you realize you have just enough time to drive your 900 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?|||momentum of the rolling cadillac = 1700 x 1 = 1700 kg mph





To counter this momentum with a 900 kg volkswagen the head -on speed of the volkswagen car should be





= 1700/900 = 1.89 mph





However you could probably just put your volkswagen in the way of the cadillac and keep your brakes jammed. That way only the fenders of both cars would probably get damaged. Or maybe a brick rolled below the cadillac's tyre would be sufficient to stop it (of course you could shout a warning to the kids to clear out of the way too).|||My speed in the VW would have to be V = (1700/900) v = (1700/900)*1 = ? mph, where v is the caddy speed. ANS This results because we want the momentum of the stuck together two cars to be P = mV - Mv = (M + m)u = 0 meaning u = 0 is the after collision speed of the two smooshed cars.





As you can see V = (M/m)v in this case. QED.|||I don't get it...