please give me detailed solution with free body diagram thank you! Problem 8.51

Question

please give me detailed solution with free body diagram thank you!

Problem 8.51 A 60 g ball is tied to the end of a 60 -cm-long string and swung in a vertical circle. The center of the circle, as shown in the figure,(Figure 1) is 150 cm above the floor. The ball is shown at the minimum speed necessary to make it over the top without the string going slack. Part A If the string is released at the instant the ball is at the top of the loop, how far to the right does the ball hit the ground? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

the required miniumu speed of the ball is

Fc= Fg

mv2/r = mg            

v = root gr = root 9.80*0.60 =  2.42m/s

the ball height when it isreleased is

150 + 60 = 210 cm = 2.10 m

from the kinmeatic equation

h = ut+ 1/2 gt^2

t = root 2h/g

= root 2 ( 2.1)/ 9.8

=0.654 s

the distance travelled by the ball from the right is x = vt = 2.42 * 0.654 = 1.58 m

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