Question

During a tennis serve, a racket is given an

Answer 1

Answer:

379.521 m/s²

Explanation:

r = Radius = 1.5 m

$\alpha$ = Angular acceleration = 160 rad/s²

$\omega$ = Angular speed = 14 rad/s

Tangential acceleration is given by

$a_t=r\alpha\\\Rightarrow a_t=1.5\times 160\\\Rightarrow a_t=240\ m/s^2$

Centripetal accelration is given by

$a_c=r\omega^2\\\Rightarrow a_c=1.5\times 14^2\\\Rightarrow a_c=294\ m/s^2$

The resultant acceleration is given by

$a=\sqrt{a_t^2+a_r^2}\\\Rightarrow a=\sqrt{240^2+294^2}\\\Rightarrow a=379.521\ m/s^2$

The magnitude of the total acceleration of the top of the racket is 379.521 m/s²