Final answer:
The acceleration of the ball when it is at its highest point is 30.383 m/s^2, and the acceleration when it is at its lowest point is 70.4167 m/s^2.
Step-by-step explanation:
In order to find the acceleration of the ball when the string is vertical and the ball is at its highest point, we can use the formula for centripetal acceleration. Centripetal acceleration is given by the equation:
a = (v^2) / r
Where a is the acceleration, v is the velocity, and r is the radius of the circular path.
At the highest point, the velocity of the ball is 4.30 m/s, and the radius of the circular path can be determined by subtracting the length of the string from the distance of the highest point to the center of the circle. Therefore, the radius is 0.6 m. Substituting these values into the equation, we get:
a = (4.30^2) / 0.6 = 30.383 m/s^2
So, the acceleration of the ball when the string is vertical and the ball is at its highest point is 30.383 m/s^2.
For the lowest point, the process is the same. The velocity of the ball is 6.50 m/s and the radius is still 0.6 m. Substituting these values into the equation, we get:
a = (6.50^2) / 0.6 = 70.4167 m/s^2
Therefore, the acceleration of the ball when the string is vertical and the ball is at its lowest point is 70.4167 m/s^2.