A student is swinging a 9 kg ball in a circular path in the vertical plane. Consider the instant when the string is horizontal as the ball is on its way up as shown in the figure. At this instant, the instantaneous tangential speed is 6 m/s, and the radius is 6 m. What is the centripetal acceleration?

centripetal acceleration = mass * velocity^2 / radius

mass = 9kg
velocity = 6 m/s
radius = 6 m
centripetal acceleration = 9 * (6)^2 / 6
centripetal acceleration = 54

To find the centripetal acceleration of the swinging ball, we need to use the formula:

Centripetal acceleration (a) = (Tangential velocity (v))^2 / Radius (r)

In this case, the tangential velocity is given as 6 m/s and the radius is 6 m.

Substituting the given values into the formula, we have:

a = (6 m/s)^2 / 6 m

Simplifying the equation, we get:

a = 36 m^2/s^2 / 6 m

Now, let's divide the numerator by the denominator:

a = 6 m/s^2

Therefore, the centripetal acceleration of the swinging ball is 6 m/s^2.