Question

A tennis player swings at a ball at a constant speed, taking 0.50 s to rotate her arms and racquet from horizontal to vertical. What acceleration is felt by a small bug at the tip of her racquet if it is 1.3 m from her shoulder

Answer 1

the acceleration of the small bug is 12.83 m/s²

Step-by-step explanation:

Given;

time of motion, t = 0.5 s

radius of the circular path created by his arm, r = 1.3 m

if he rotates his arm from horizontal to vertical, the angular displacement = 90⁰

The centripetal acceleration of the ball is calculated as;

`a_c = \omega^2 r\\\\a_c = ((\theta)/(t) )^2 r\\\\`

`a_c = ((90)/(360) *( 2\pi )/(t) )^2r\\\\a_c = ((\pi)/(2t) )^2 r\\\\a_c = (\pi^2r)/(4t^2) = (\pi^2 *1.3 )/(4* 0.5^2) = 12.83 \ m/s^2`

Therefore, the acceleration of the small bug is 12.83 m/s²