Question

A hockey player receives a corner shot at a speed of $15\text{m/s}$ at angle ${30}^{\circ }$ with y - axis and then shoots the ball along x - axis with the speed $30\text{m/s}$. If the mass of the ball is $150\text{grams}$ and it remains in contact with the hockey stick for $0.01\text{s}$, the force exerted on the ball along x - axis is

• A. $281\text{N}$
• B. $187.5\text{N}$
• C. $562.5\text{N}$
• D. $375\text{N}$

Answer 1

The correct option is C $562.5\text{N}$


Using Newton's second law, force exerted on the ball in the x-direction,
$F_x=\frac{d{P}_x}{dt}=\frac{\Delta P}{\Delta t}$
Initial and final momentum direction of the ball can be show as

Initial momentum in x-direction,
$P_{ix}=P_{i}sin{30}^{\circ }=\frac{P_i}{2}$
Change in momentum in x-direction,
$\Delta P_x=P_f-P_{ix}=-P_f-P_i/2$
Since $\overrightarrow{P}=m\overrightarrow{v}$
$\begin{array}{}\Delta P_x=-m{v}_f-m{v}_i/2& \text{(1)}\end{array}$
$v_f=30m/s$ and $v_i=15m/s$
Therefore,
$\Delta P_x=-m{v}_f-m{v}_i/2=-5.625kgm/s$
Hence
$F_x=\frac{-5.625}{0.01}=-562.5N$
thus the magnitude of force in x-direction is 562.5 N.