Answer
(a) The ratio of the final magnitude of the momentum to the initial magnitude of the momentum is 3
(b) The ratio of the final kinetic energy to the initial kinetic energy is 9
Work Step by Step
(a) We can find the ratio of the final magnitude of the momentum to the initial magnitude of the momentum:
$\frac{p_f}{p_0} = \frac{mv_f}{mv_0} = \frac{3v_0}{v_0} = 3$
The ratio of the final magnitude of the momentum to the initial magnitude of the momentum is 3
(b) We can find the ratio of the final kinetic energy to the initial kinetic energy:
$\frac{KE_f}{KE_0} = \frac{\frac{1}{2}mv_f^2}{\frac{1}{2}mv_0^2} = \frac{(3v_0)^2}{v_0^2} = 9$
The ratio of the final kinetic energy to the initial kinetic energy is 9
