If a person can jump on the earth surface upto a height 2 m . His jump on a satellite where acceleration due to gravity is `1.96 m //s^2` will be -

Options

A. 5 m
B. 10 m
C. 20 m
D. 2 m

Answer

To solve the problem, we need to determine how high a person can jump on a satellite where the acceleration due to gravity is 1.96 m/s², given that they can jump 2 meters on Earth's surface.

### Step-by-Step Solution:

1. **Understanding the Jump Height on Earth:**
The maximum height \( h \) a person can jump on Earth is given as 2 meters. This height can be related to the acceleration due to gravity on Earth, which is approximately \( g_e = 9.8 \, \text{m/s}^2 \).

2. **Using the Formula for Maximum Jump Height:**
The maximum height \( h \) that a person can jump is given by the formula:
\[ h = \frac{v^2}{2g} \]
where \( v \) is the initial velocity and \( g \) is the acceleration due to gravity. Rearranging this formula gives us:
\[ v = \sqrt{2gh} \]

3. **Calculating the Initial Velocity on Earth:**
For the jump height of 2 meters on Earth:
\[ v_e = \sqrt{2 \cdot 9.8 \cdot 2} = \sqrt{39.2} \approx 6.26 \, \text{m/s} \]

4. **Determining the Jump Height on the Satellite:**
Now, we will use this initial velocity to find out how high the person can jump on the satellite where the acceleration due to gravity \( g_s = 1.96 \, \text{m/s}^2 \).
Using the same formula for maximum height:
\[ h_s = \frac{v^2}{2g_s} \]
Substituting \( v \) from the previous calculation:
\[ h_s = \frac{(6.26)^2}{2 \cdot 1.96} \]
\[ h_s = \frac{39.1876}{3.92} \approx 10 \, \text{m} \]

5. **Final Result:**
Therefore, the height the person can jump on the satellite is approximately **10 meters**.