Question

A tennis player receives a shot with the ball (0.0600 kg) traveling horizontally at 50.4 m/s and returns the shot with the ball traveling horizontally at 37.0 m/s in the opposite direction. (Take the direction of the ball's final velocity (toward the net) to be the +x-direction.)
(a) What is the impulse delivered to the ball by the racket?
(b) What work does the racket do on the ball? (Indicate the direction with the sign of your answer.)

Answer 1

(a) The impulse delivered to the ball by the racket is 5.24 kg.m/s

(b) The work that the racket does on the ball is -35.1 Joule

Further Explanation

Given :

mass of ball = m = 0.06 kg

initial velocity = v₁ = -50.4 m/s

final velocity = v₂ = 37.0 m/s

Unknown :

(a) Impulse = I = ?

(b) Work = W = ?

Solution :

Question (a) :

In this question , we could use the formula from Second Law of Newton :

$I = \Delta p$

$I = p_2 - p_1$

$I = m \times v_2 - m \times v_1$

$I = m \times (v_2 - v_1)$

$I = 0.06 \times (37.0 - (-50.4))$

$I = 0.06 \times (87.4)$

$I = 5.244~kg.m/s$

$\large { \boxed {I \approx 5.24~kg.m/s} }$

Question (b) :

$W = F \times d$

$W = (\frac{I}{\Delta t})(\frac {v_1 + v_2}{2} \Delta t)$

$W = \frac{I(v_1 + v_2)}{2}$

$W = \frac{5.244(-50.4 + 37)}{2}$

$W = \frac{5.244(-13.4)}{2}$

$W = -35.1348~Joule$

$\large { \boxed {W \approx -35.1~Joule}}$

Learn more

Newton's Law of Motion: brainly.com/question/10431582

Example of Newton's Law: brainly.com/question/498822

Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

Keywords: Newton, Law, Impulse, Work