Conservation of Momentum EX 4

(a) The momentum of the truck, $p$, is:

$p=mv=(10^4)(30)=3\times 10^5\frac{kgm}{s}$

The momentum of the car, $p^{\prime }$, is equal to the momentum of the truck, $p$:

$p^{\prime }=p=3\times 10^5=m^{\prime }{v}^{\prime }=(1.2\times 10^3)v^{\prime }$

Solve for $v^{\prime }$:

$v^{\prime }=\frac{3\times 10^5}{1.2\times 10^3}=2.5\times 10^{2}m/s$

(b) The kinetic energy of the truck, $K$, is:

$K=\frac{1}{2}m{v}^2=\frac{1}{2}(10^4)(30{)}^2=4.5\times 10^{6}J$

The kinetic energy of the car, $K^{\prime }$, is equal to the kinetic energy of the truck, $K$:

$K^{\prime }=K=4.5\times 10^6=\frac{1}{2}{m}^{\prime }{v^{\prime }}^2=\frac{1}{2}(1.2\times 10^3){v^{\prime }}^2$

Solve for $v^{\prime }$:

$v^{\prime }=\sqrt{\frac{2\times 4.5\times 10^6}{1.2\times 10^3}}=86.6m/s$