Question

A hockey ball of mass 200g traveling at 10m/s is struck by a hockey stick so as to return it along its original path with a velocity of $5m/s$. Calculate the change of momentum that occurred in the motion of the hockey ball by the force applied by the hockey stick.

Answer 1

Hint: The momentum of an object is given by the product of the velocity of the object and the mass of the object. Since velocity is a vector quantity, momentum is also a vector quantity.

Complete step-by-step answer:
Following information is given in the question
Mass of the hockey ball, $m = 200g = \dfrac{{200}}{{1000}}kg = 0.2kg$
Initial velocity of the ball, $u = 10m/s$
Final velocity of the ball, $v = - 5m/s$
Here, we take the final velocity of the hockey ball to be negative because it is given in the question that the ball has to be set back on its original path that is in the opposite direction. This is a crucial property of vectors. If we reverse the direction of a vector (say $\overrightarrow A $) then, we can write this reversed vector as $ - \overrightarrow A $.
We know that,
Momentum is given by $P = mv$
Initial momentum, ${P_1} = 0.2 \times 10 = 2kgm/s$
Final momentum, ${P_2} = 0.2 \times ( - 5) = - 10kgm/s$
Change in momentum $ = {P_1} - {P_2}$
$ = 2 - ( - 1)$
$ = 3kgm/s$

$\therefore $ The change in momentum of the hockey stick $ = 3kgm/s$.

Note:
When the ball hits the hockey stick, both the ball and the hockey stick apply some impulsive force on each other. This force is equal to the change in the momentum of either hockey ball or hockey stick. We call this force impulsive because it acts for a very short amount of time on both the ball and the stick.