Answer
The magnitude of the total acceleration is $380m/s^2$
Work Step by Step
The radius of the rotation circle is the distance between the racket top and the shoulder $r=1.5m$
We have $\alpha=160rad/s^2$. At the top of the serve, we also know $\omega=14rad/s$, so
- The racket's tangential acceleration: $a_T=r\alpha=240m/s^2$
- The racket's centripetal acceleration: $a_c=r\omega^2=294m/s^2$
Since these two acceleration vectors are perpendicular with each other, the sum of them, which is the total acceleration, is $$a=\sqrt{a_T^2+a_c^2}=380m/s^2$$
