A ball on the end of a string is whirled around in a horizontal circle of radius 0.22 m. The plane of the circle is 1.69 m above the ground. The string breaks and the ball lands 2.68 m away from the point on the ground directly beneath the ball’s location when the string breaks.

The acceleration of gravity is 9.8 m/s2 .
Find the centripetal acceleration of the ball during its circular motion.

so do i start by calculating the centripetal acceleration?

i figured it out if anyone would like me to work out the process let me know =]

Yes, to find the centripetal acceleration of the ball during its circular motion, you can start by calculating it.

The centripetal acceleration of an object moving in a circle is given by the formula:

ac = v^2 / r

where ac is the centripetal acceleration, v is the linear velocity of the object, and r is the radius of the circle.

In this case, you are given the radius of the circle (0.22 m). However, you haven't been provided with the linear velocity of the ball.

To find the linear velocity, you need to use another equation. The distance travelled by the ball before it lands is given as 2.68 m. By applying some trigonometry, you can find the horizontal component of the velocity.

Since the ball is moving in a horizontal circle, the horizontal component of its velocity remains constant throughout the motion. Let's call this constant horizontal velocity vh.

Using the formula for horizontal distance:

d = vh * t

where d is the horizontal distance (2.68 m) and t is the time taken by the ball to travel that distance.

We can rearrange the equation to solve for t:

t = d / vh

Now, we need to find vh. The vertical motion of the ball is due to gravitational acceleration. The time taken for the ball to land can be calculated using the equation:

y = (1/2) * g * t^2

where y is the height of the circular motion plane above the ground (1.69 m) and g is the acceleration due to gravity (9.8 m/s^2). Let's call this time tland.

Substituting the values into the equation:

1.69 = (1/2) * 9.8 * tland^2

Now solve the equation for tland.

Once you have tland, you can substitute it back into the equation t = d / vh to solve for vh.

Now that you have the horizontal component of velocity (vh), you can calculate the centripetal acceleration using the formula mentioned earlier:

ac = v^2 / r

Substitute vh for v and the given radius of the circle (0.22 m) for r to find the centripetal acceleration.