During your tennis serve, your racket and arm move in an approximately rigid arc with the top of the racket 1.5 m from your shoulder joint. The top accelerates from rest to a speed of 20 m/s in a time interval of 0.10 s. A) Determine the magnitude of the average tangential acceleration of the top of the racket. B) Determine the magnitude of the rotational acceleration of your arm and racket.

(A). The average tangential acceleration of the top of the racket is 200 m/s².

(B). The magnitude of the rotational acceleration of your arm and racket is 133.3 rad/s²

Explanation:

Given that,

Speed = 20 m/s

Time = 0.10 sec

Distance r= 1.5 m

(A). We need to calculate the average tangential acceleration of the top of the racket

Using equation of motion

Here, u =0

Put the value into the formula

The average tangential acceleration of the top of the racket is 200 m/s².

(B). We need to calculate the magnitude of the rotational acceleration of your arm and racket

Using formula of rotational acceleration

Put the value into the formula

The magnitude of the rotational acceleration of your arm and racket is 133.3 rad/s²

Hence, (A). The average tangential acceleration of the top of the racket is 200 m/s².

(B). The magnitude of the rotational acceleration of your arm and racket is 133.3 rad/s²

the maxium height is 34m/s