Tennis Head Ties
Physics Help!?
A boy ties a 58g tennis ball to the end of a string that is .65m long and whirls the ball above his head in a horizontal circle. The boy exerts a force of 5.2N on the string to keep the ball moving in a circle at a height of 1.7m above the ground. Deternine the speed of the ball. Describe the motion of the ball the instant the string breaks. The motion of the ball after the string breaks but before it hits the ground. How long will it take the ball to reach the ground? How far will the ball travel horizontally before it hits the ground?
the angle with the vertical of the string is
5.2*cosθ=0.058*9.8
solve for θ
θ=acos(0.058*9.8/5.2)
θ=83.72 degrees
sinθ*5.2=m*v^2/r
solve for v
v=sqrt(r*sinθ*5.2/m)
we need r, which is the radius of the circle
r=0.65*sinθ
v=sinθ*sqrt(0.65*5.2/0.058)
v=7.59 m/s
When the string breaks, the ball becomes a free falling projectile starting form a height of 1.7m with vy=0 and vx=7.59 m/s
the time to impact is
t=sqrt(2*1.7/9.8)
0.589 s
the range is
7.59*0.589
4.47 m
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