A body projected vertically upwards with a velocity of `19.6 m//s` reaches a height of 19.8 m on earth. If it is projected vertically up with the same velocity on moon, then the maximum height reached by it is

Options

A. 19.18 m
B. 3.3 m
C. 9.9 m
D. 118.8 m

Explanation

To solve the problem step by step, we will use the kinematic equations of motion.

### Step 1: Understand the problem
We have a body projected vertically upwards with an initial velocity of \( u = 19.6 \, \text{m/s} \) on Earth, and it reaches a maximum height of \( h = 19.8 \, \text{m} \). We need to find the maximum height reached by the same body when projected on the Moon with the same initial velocity.

### Step 2: Use the kinematic equation
The kinematic equation we will use is:
\[ v^2 = u^2 + 2as \]
where:
- \( v \) is the final velocity (0 m/s at maximum height),
- \( u \) is the initial velocity (19.6 m/s),
- \( a \) is the acceleration (which will be negative due to gravity),
- \( s \) is the displacement (maximum height).

### Step 3: Find the acceleration due to gravity on Earth
On Earth, the acceleration due to gravity \( g \) is approximately \( 9.8 \, \text{m/s}^2 \).

### Step 4: Calculate the maximum height on Earth
Using the equation:
\[ 0 = (19.6)^2 + 2(-9.8)(19.8) \]
Rearranging gives:
\[ 19.8 = \frac{(19.6)^2}{2 \cdot 9.8} \]
This confirms that the height reached on Earth is indeed \( 19.8 \, \text{m} \).

### Step 5: Find the acceleration due to gravity on the Moon
The acceleration due to gravity on the Moon is approximately \( g' = \frac{g}{6} = \frac{9.8}{6} \approx 1.63 \, \text{m/s}^2 \).

### Step 6: Calculate the maximum height on the Moon
Using the same kinematic equation for the Moon:
\[ v^2 = u^2 + 2a s \]
Substituting \( v = 0 \), \( u = 19.6 \, \text{m/s} \), and \( a = -g' \):
\[ 0 = (19.6)^2 + 2(-1.63)s \]
Rearranging gives:
\[ s = \frac{(19.6)^2}{2 \cdot 1.63} \]

### Step 7: Calculate the value
Calculating \( s \):
\[ s = \frac{384.16}{3.26} \approx 117.8 \, \text{m} \]

### Conclusion
The maximum height reached by the body when projected on the Moon is approximately \( 118 \, \text{m} \).