Acceleration of a Tennis Racket?

Question

During a serve, a tennis racket of mass 1.1 kg is given an angular acceleration of 160 rad/sec2. At the top of the serve, the racket has an angular speed of 14 rad/sec.

If the distance between the top of the racket and the shoulder is 1.4 m, what is the total acceleration of the top of the racket?

Answer 1

I think we have to components of acceleration. One tangential and the other centripetal

Tangential acceleration equal to the product of a radius and angular acceleration

at= rA

Normal to the path or centripetal acceleration ac is tangential velocity squared over radius of the path
ac=V^2/r

The tangential velocity V is a product of radius of the path and angular velocity (speed)
V= r w
now
ac=r ^2 w^2

at=sqrt(ac^2 + at^2)
angle=atan(ac/at)

have fun