A body is projected upwards under gravity with a speed of 19.6 Then, maximum height which can be reached is

Options

A. 4.9 m
B. 19.6 m
C. 9.8 m
D. 39.2 m

Explanation

To solve the problem of finding the maximum height reached by a body projected upwards with an initial speed of 19.6 m/s under the influence of gravity, we can use the following steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial velocity (u) = 19.6 m/s
- Final velocity (v) at maximum height = 0 m/s (since the body stops rising at the maximum height)
- Acceleration due to gravity (g) = 9.8 m/s² (acting downwards)

2. **Use the Kinematic Equation:**
We will use the third equation of motion:
\[ v^2 = u^2 - 2gh \]
where:
- \(v\) = final velocity
- \(u\) = initial velocity
- \(g\) = acceleration due to gravity
- \(h\) = maximum height

3. **Substitute the Known Values:**
Since \(v = 0\) at maximum height, we can substitute the values into the equation:
\[ 0 = (19.6)^2 - 2 \cdot 9.8 \cdot h \]

4. **Rearranging the Equation:**
Rearranging the equation to solve for \(h\):
\[ 2 \cdot 9.8 \cdot h = (19.6)^2 \]
\[ h = \frac{(19.6)^2}{2 \cdot 9.8} \]

5. **Calculate \(h\):**
First, calculate \( (19.6)^2 \):
\[ (19.6)^2 = 384.16 \]
Now substitute this value into the equation:
\[ h = \frac{384.16}{2 \cdot 9.8} \]
\[ h = \frac{384.16}{19.6} = 19.6 \text{ m} \]

6. **Conclusion:**
The maximum height \(h\) that the body can reach is **19.6 meters**.