The acceleration due to gravity on the planet A is $9$ times the acceleration due to gravity on planet B. A ma

Question

The acceleration due to gravity on the planet A is $9$ times the acceleration due to gravity on planet B. A man jumps to a height of $2 	ext{ m}$ on the surface of A. What is the height of jump by the same person on the planet B?

Accepted Answer

1. **Identify the Principle:** The height $H$ reached by a person jumping vertically depends on the initial velocity $u$ (supplied by the person's energy) and the acceleration due to gravity $g$. Using the kinematic equation $v^2 = u^2 - 2gH$ (where final velocity $v=0$ at max height), we get:
   $$ H = \frac{u^2}{2g} $$
2. **Analyze the Relationship:** Assuming the person exerts the same effort, the initial velocity $u$ remains constant on both planets. Therefore, the height reached is inversely proportional to gravity ($H \propto \frac{1}{g}$).
   $$ H_A g_A = H_B g_B $$
3. **Substitute Values:**
   - Given: $g_A = 9 g_B$ and $H_A = 2 	ext{ m}$.
   - Substitute into the equation:
     $$ 2 	imes (9 g_B) = H_B 	imes g_B $$
     $$ 18 g_B = H_B g_B $$
     $$ H_B = 18 	ext{ m} $$
   .

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