Question

A juggler throws balls into air, He throws one whenever s highest the previous one is at its highest point. How high do the ball rise if he throws n balls each sec? acceleration due to gravity is g.

Answer 1

A juggler throws balls into air, He throws one whenever $s$ highest the previous one is at its highest point. How high do the balls rise if he throws $n$ balls each sec? Acceleration due to gravity is $g$.

If he throws n balls each sec, therefore, the time required to reach the highest point equals:

$$t = \frac {1}{n} \sec$$

Coordinate for uniformly accelerated motion equals:

$$h = v _ {0} t - \frac {g t ^ {2}}{2}$$

$v_{0}$ - initial velocity of the ball

$g$ - gravitational acceleration

$t$ - time

$$h = v _ {0} t - \frac {g t ^ {2}}{2} = v _ {0} t - g t ^ {2} + \frac {g t ^ {2}}{2} = (v _ {0} - g t) t + \frac {g t ^ {2}}{2}$$

If $t = \frac{1}{n} s v_0 - gt = v = 0$ - maximum height

$$h = \frac {g t ^ {2}}{2} = \frac {g}{2 n ^ {2}}$$

Answer: $h = \frac{g}{2n^2}$