Question

To warm up for a match, a tennis player hits the 58.0 g ball vertically with her racket. If the ball is stationary just before it is hit and goes 5.50 m high, what impulse did she impart to it?

Answer 1

Answer:

$J=0.602\ kg-m/s$

Explanation:

Given that,

Mass of the ball, m = 58 g

To find,

Impulse did she impart to it

Solution,

Let u is the initial speed of the ball. Using equation of kinematics as :

At 5.5 m, v = 0

So, $v^2=u^2+2ah$

Here, a = -g

$v^2=u^2-2gh$

$u=\sqrt{2gh}$

$u=\sqrt{2\times 9.8\times 5.5}$

u = 10.38 m/s

Since, the ball is stationary just before it is hit, $p_1=0$

$p_2=mv$

$p_2=58\times 10^{-3} \times 10.38=0.602\ kg-m/s$

According to impulse- momentum theorem, the impulse imparted is equal to the change in momentum. So,

$p=0.602\ kg-m/s$

So, the impulse did impart to it is 0.602 kg-m/s. Hence, this is the required solution.