A particle is thrown vertically upward. Its velocity at half of the maximum height is $10 ext{ m/s}

Question

A particle is thrown vertically upward. Its velocity at half of the maximum height is $10	ext{ m/s}$. What is the maximum height attained by it? (Take $g = 10	ext{ m/s}^2$)

Professor PC Thomas Classes · Answer

Let the maximum height be $H$. The initial velocity $u$ relates to $H$ by $u^2 = 2gH$. At height $h = \frac{H}{2}$, the velocity $v$ is given by $v^2 = u^2 - 2g(\frac{H}{2}) = 2gH - gH = gH$. Given $v = 10	ext{ m/s}$, we have $10^2 = 10 	imes H \implies 100 = 10H \implies H = 10	ext{ m}$.