Question

A stone thrown vertically upwards with a speed of 5 m/sec attains a height $H_1$. Another stone thrown upwards from the same point with a speed of 10 m/sec attains a height $H_2$. The correct relation between $H_1$ and $H_2$ is

• A. $H_2 = 4 H_1$
• B. $H_2 = 3 H_1$
• C. $H_1 = 2 H_2$
• D. $H_1 = H_2$

Answer 1

Answer: (A)

$H_2 = 4 H_1$

Answer 2

From third equation of motion $v^2 = u^2 + 2ah$ In first case initial velocity $u_1 = 5 \, m/ \sec$ final velocity $v_1 = 0, a = - g$ and max. height obtained is $H_1$, then, $H_1 = \frac{25}{2g}$ In second case $u_2 = 10 \, m/ \sec, v_2 = 0, a = -g$ and max. height is $H_2$ then, $H_2 = \frac{100}{2g}$ It implies that $H_2 = 4H_1$