Answer:
379.521 m/s²
Explanation:
r = Radius = 1.5 m
[tex]\alpha[/tex] = Angular acceleration = 160 rad/s²
[tex]\omega[/tex] = Angular speed = 14 rad/s
Tangential acceleration is given by
[tex]a_t=r\alpha\\\Rightarrow a_t=1.5\times 160\\\Rightarrow a_t=240\ m/s^2[/tex]
Centripetal accelration is given by
[tex]a_c=r\omega^2\\\Rightarrow a_c=1.5\times 14^2\\\Rightarrow a_c=294\ m/s^2[/tex]
The resultant acceleration is given by
[tex]a=\sqrt{a_t^2+a_r^2}\\\Rightarrow a=\sqrt{240^2+294^2}\\\Rightarrow a=379.521\ m/s^2[/tex]
The magnitude of the total acceleration of the top of the racket is 379.521 m/s²
