The ball goes high!

Classical Mechanics Level 2

A juggler throws balls into the air. He throws one whenever the previous one is at its highest point. If he throws n n balls each second, then which of the following gives us the hieght attained by each of the ball.

g 4 n 2 \frac{g}{4n^{2}} g 2 n 2 \frac{g}{2n^{2}} g n \frac{g}{n} 2 g n 2 \frac{2g}{n^{2}}

Umang Vasani by Umang Vasani , 24, India

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1 solution

Umang Vasani
Jun 4, 2014

Time taken by each ball to rise to the highest point is given as 1 n \frac{1}{n} . We take final velocity of the first ball when it reaches the highest point as zero . Acceleration due to gravity is − g -g Using the equation of motion in one dimension, v = u + a t v = u + at Substituting v = 0 , a = − g , t = 1 n v = 0, a = -g, t = \frac{1}{n} Thus we get u = g n u = \frac{g}{n} Also as v 2 = u 2 + 2 a h v^{2} = u^{2} + 2ah we get h = g 2 n 2 h = \frac{g}{2n^{2}} by substituting v = 0 , a = − g , u = g n v = 0, a = -g, u = \frac{g}{n}

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i am not satisfied

Vatsal Patel - 6 years, 11 months ago

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