Aboy whirls a stone in a horizontal circle of radius 1.8 m and at height 1.8 m above level ground. the string breaks, and the stone flies off horizontally and strikes the ground after traveling a horizontal distance of 9.9 m. what is the magnitude of the centripetal acceleration of the stone while in circular motion?

Acceleration is

Solution:

As per the question:

Radius of the circle, R = 1.8 m

Height above the ground, h = 1.8 m

Horizontal distance, x = 9.9 m

Now,

The magnitude of the centripetal acceleration can be calculated as:

where

v = velocity

R = radius

= centripetal acceleration

Now, if we consider the vertical component of motion only, then considering the initial velocity, 'u' = 0, from kinematic eqn:

t = 0.606 s

Now, for the horizontal component of velocity:

x = vt

Now, we know that the centripetal acceleration is given by: