A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is
Select the correct option:
A
$\frac{g}{2 n}$
B
$\frac{\mathrm{g}}{\mathrm{n}}$
C
2 gn
D
$\frac{\mathrm{g}}{2 \mathrm{n}^2}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Time taken by ball to reach highest point $=\frac{\mathrm{u}}{\mathrm{g}}$
Frequency of throw $=\frac{\mathrm{g}}{\mathrm{u}}=\mathrm{n}$
$$
\begin{aligned}
& \Rightarrow u=\frac{g}{n} \\
& H_{\max }=\frac{u^2}{2 g}=\frac{\left(\frac{g}{n}\right)^2}{2 g} \frac{g}{2 n^2}
\end{aligned}
$$
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