question_answer

A hockey player receives a corner shot at a speed of 15 m/s at an angle of 30° with the y-axis and then shoots the ball of mass 100 g along the negative x-axis with a speed of 30 m/s. 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)         187.5N

C)  562.5 N               

D)         375 N

Correct Answer: D

Solution :

If a constant force\[\overset{\to }{\mathop{F}}\,\]is applied on a body for short interval of time\[\Delta t\], then the impulse this force is\[F\times \Delta t\]. Since, impulse = change in momentum\[(\Delta p)\] \[\therefore \]  \[F\times \Delta t=\Delta p\] \[\Rightarrow \]               \[F=\frac{\Delta p}{\Delta t}\] Change in \[x-\]direction                 \[F=\frac{m[30-(-15\sin {{30}^{o}})]}{0.01}\]                 \[F=\frac{0.1\times 37.5}{0.01}=375\,\,N\] Note: Unit of impulse is same as that of momentum.