Question

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

• A. $281\text{N}$
• B. $187\text{N}$
• C. $562.5\text{N}$
• D. $375\text{N}$

Answer 1

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

Mass of ball, $m=150\text{gm}=0.15\text{kg}$
Let $v_{2x}$ be the final velocity of ball along $x$ - axis
$v_{1x}$ and $v_{1y}$ be the components of intial velocity of the ball along x - axis and y-axis respectively.
The situation is shown in the figure.


$v_{1x}=-v_1\cos {60}^{\circ }=-\frac{15}{2}\text{m/s}$
and $v_{2x}=30\text{m/s}$
We know, $F=\frac{\Delta P}{\Delta t}$
Net average force acting on ball along $x$ - axis is $F_x$
$F_x=\frac{\Delta P_x}{\Delta t}=\frac{P_f-P_i}{\Delta t}=\frac{m{v}_{2x}-m{v}_{1x}}{\Delta t}$
$\Rightarrow F_x=\frac{m[v_{2x}-v_{1x}]}{\Delta t}=\frac{0.150[30-(-15\cos {60}^{\circ }\left)\right]}{0.01}$

$\therefore F_x=\frac{0.15\times 37.5}{0.01}=562.5\text{N}$