Question

A hockey player receives a corner shot at a speed of $15m{s}^{-1}$ at an angle of $30°$ with the y – axis and then shoots the ball of mass $100g$ along the negative x-axis with a speed of $30m{s}^{-1}$. If it remains in contact with the hockey stick for $0.01s$, the force imparted to the ball in the x-direction is

• A. $281.25N$
• B. $187.5N$
• C. $562.5N$
• D. $375N$

Answer 1

The correct option is D

$375N$

Explanation for the correct option:

Step 1: Given data:

Mass of the ball, $m=100g=0.1Kg$

Initial velocity of the ball, $u=15m/s$ at an angle,$\theta =30°$

Final velocity of the ball, $v=30m/s$ along x-axis

Step 2: Finding the force exerted by the ball:

Change in momentum of ball along x- axis $\Delta P=mv–mu$

$\Rightarrow \Delta P=mv–\left[m(-u\sin 30°)\right]$………..(As the momentum is along x-axis)

$$\begin{gathered} \Rightarrow \Delta P=mv+m\left(u\sin 30°\right) \\ \Rightarrow \Delta P=(0.1x30)+0.1(15x0.5) \\ \Rightarrow \Delta P=3+0.75 \\ \Rightarrow \Delta P=3.75 \end{gathered}$$

Hence, Force exerted by the ball $=\frac{∆P}{t}$

$$\begin{gathered} =\frac{3.75}{0.01} \\ =375N \end{gathered}$$

Hence, option D is correct.