Question

The fastest server in women's tennis is Venus Williams, who recorded a serve of 204 km/h at the French Open in 2007. Suppose that the mass of her racket was 331g and the mass of the ball was 56.0g. If her racket was moving at 200 km/h when it hit the ball, approximately what was the racket's speed after hitting the ball?

Answer 1

Answer:

45.96844 m/s

Explanation:

$m_1$ = Mass of racket = 331 g

$m_2$ = Mass of ball = 56 g

$u_1$ = Initial velocity of racket = 200 km/h

$u_2$ = Initial velocity of ball = 0

$v_1$ = Final velocity of racket

$v_2$ = Final velocity of ball = 204 km/h

In this system the linear momentum is conserved

$m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\Rightarrow v_1=\dfrac{m_1u_1+m_2u_2-m_2v_2}{m_1}\\\Rightarrow v_1=\dfrac{0.331\times \dfrac{200}{3.6}+0.056\times 0-0.056\times \dfrac{204}{3.6}}{0.331}\\\Rightarrow v_1=45.96844\ m/s$

The velocity of racket after hitting the ball is 45.96844 m/s