Question

A hockey ball of mass 200 g travelling at $10m{s^{ - 1}}$ is struck by a hockey stick so as to return it along its original path with a velocity of$5m{s^{ - 1}}$. Calculate the change of momentum which occurred in the motion of the hockey ball by the force applied by the hockey stick:
A) -3 Ns.
B) 3 Ns.
C) 6 Ns.
D) -6 Ns.

Answer 1

Hint: Momentum is defined as the product of mass and velocity. The rate of change of momentum with respect to time is known as force. The force is defined as the product of mass and acceleration of the body and unit of force is Newtons.

Formula Used: The formula of momentum is given by,
$ \Rightarrow p = m \cdot v$
Where p is the momentum the mass is m and the velocity is v.

Complete step by step answer:
It is given in the problem that a hockey ball of mass 200 g travelling at $10m{s^{ - 1}}$ is struck by a hockey stick so as to return it along its original path with a velocity of $5m{s^{ - 1}}$ and we need to calculate the change in the momentum of the hockey ball.
The formula of momentum is given by,
$ \Rightarrow p = m \cdot v$
Where p is the momentum the mass is m and the velocity is v.
The mass of the hockey ball is 200 g and the initial velocity of the ball is $10m{s^{ - 1}}$ and the final velocity of the ball is $5m{s^{ - 1}}$ in the opposite direction of the initial direction. The change in the momentum is given by,
$\Delta p = m\left( {v - u} \right)$
Where $\Delta p$ is change in momentum mass is m initial and final velocity of the hockey ball is u and v respectively.
The change in momentum of hockey ball is equal to,
$ \Rightarrow \Delta p = m\left( {v - u} \right)$
$ \Rightarrow \Delta p = \left( {\dfrac{{200}}{{1000}}} \right) \cdot \left[ {5 - \left( { - 10} \right)} \right]$
\[ \Rightarrow \Delta p = \left( {0 \cdot 2} \right) \cdot \left( {15} \right)\]
\[ \Rightarrow \Delta p = 3Ns\]
The change in the momentum is\[\Delta p = 3Ns\].
The correct answer for this problem is option B.

Note: Momentum is a vector quantity and therefore if there is change in line of motion of the body then we calculate the momentum along the same directions. The velocity of the hockey ball is negative while returning towards its original path.