A juggler throws ball vertically upwards with same initial velocity in air. When the first ball reaches its highest positions he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

<p>Time to reach at max height t = <math><mrow><mfrac><mrow><mi>u</mi></mrow><mrow><mi>g</mi></mrow></mfrac><mi>n</mi><mi>o</mi><mo>.</mo></mrow></math>&nbsp;of balls thrown in 1 sec = n.</p><p>So, time taken by each ball to reach maxm height, =&nbsp;<math><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mi>s</mi><mi>e</mi><mi>c</mi></mrow></math></p><p>i.e.&nbsp;<math><mrow><mfrac><mrow><mi>u</mi></mrow><mrow><mi>g</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>⇒</mo><mi>u</mi><mo>=</mo><mfrac><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></math>&nbsp;So, hmax =&nbsp;<math><mrow><mfrac><mrow><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn><mi>g</mi></mrow></mfrac></mrow></math></p><p>=&nbsp;<math><mrow><mfrac><mrow><msup><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn><mi>g</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></math></p><p><math><mrow><mo>=</mo><mfrac><mrow><mi>g</mi></mrow><mrow><mn>2</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></math></p>

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