Question

The parking brake on a 1000 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 2000 kg Volkswagen head-on into the Cadillac and save the children. You may want to review (Page 269) . Part A With what speed should you impact the Cadillac to bring it to a halt?

Answer 1

Answer:

0.5 mph in the opposite direction

Explanation:

$m_1$ = Mass of Cadillac = 1000 kg

$v_1$ = Velocity of Cadillac = 1 mph

$m_2$ = Mass of Volkswagen = 2000 kg

$v_2$ = Velocity of Volkswagen

In order to know the speed the system must have the momentum exchange

As the linear momentum of the system is conserved

$m_1v_1+m_2v_2=0\\\Rightarrow v_2=-\dfrac{m_1v_1}{m_2}\\\Rightarrow v_2=\dfrac{1000\times 1}{2000}\\\Rightarrow v_2=-0.5\ mph$

The speed of the impact is given by 0.5 mph in the opposite direction