Any explanations are appreciated! You whirl a ball tied to a light string of neg

Question

Any explanations are appreciated!

You whirl a ball tied to a light string of negligible mass in a vertical circle in the clockwise direction. The mass of the ball is 0.140 kg and the length of the string is 0.680 m. You maintain the center of the circle to be at a constant height of 2.66 m from the floor. If the string breaks when the ball is at the lowest point and its speed is 1.80 m/s, where on the floor does it land? Express your answer in vector form with the center of the circle as the origin.

d = m

Explanation / Answer

from the vertical motion

Y = ( g t2 ) / 2 ----> t = sqrt{ ( 2 y ) / g } = sqrt{ ( 2 * ( 2.66 m - 0.680 m )) / ( 9.81 m/s2 ) } = 0.404 s

then, the horizontal distance is

x = v t = ( 1.80 m/s )( 0.404 s ) = 0.727 m

hence the position of the ball is

d = 0.727 m i + 2.66 m j

the position is relative to the center of the circle

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