Q. A hockey player receives a corner shot at a speed of ${15\ ms\ }^{- 1}$at an angle of $30{^\circ}$ with the $y$-axis and then shoots the ball of mass 100 g along the negative $x$-axis with a speed of ${30\ ms}^{- 1}$. If it remains in contact with the hockey stick for 0.01 s, the force imparted to the ball in the $x$-direction is
A) 281.25 N
B) 187.5 N
C) 562.5 N
D) 375 N
Explanation
(d) If a constant force F is applied on a body for a short interval of time $\mathrm{\Delta}t,$ then the impulse of this force is $F \times \mathrm{\Delta}t$
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Since, impulse = change in momentum $(\mathrm{\Delta}p)$
$\therefore\ \ F \times \mathrm{\Delta}t = \mathrm{\Delta}p$
$\Longrightarrow \ \ F = \frac{\mathrm{\Delta}p}{\mathrm{\Delta}t}$
Change in $x$-direction
$F = \frac{m\lbrack 30 - ( - 15\sin{30{^\circ})\rbrack}}{0.01}$
$F = \frac{0.1 \times 37.5}{0.01} = 375\ N$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.