The velocity of a body moving vertically up is `49 ms^(-1)` at half the maximum height. The height to which it could further rise is

Options

A. 245 m
B. 122.5 m
C. 61.25 m
D. none

Answer

To solve the problem, we need to determine the maximum height that a body can reach when it is moving vertically upwards, given its velocity at half of that maximum height.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We know that the body has a velocity of \(49 \, \text{m/s}\) at half of the maximum height. Let's denote the maximum height as \(H\). Therefore, at half the maximum height, the height is \(H/2\).

2. **Using the Kinematic Equation**:
- We will use the kinematic equation:
\[ v^2 = u^2 + 2as \]
where:
- \(v\) = final velocity (0 m/s at maximum height),
- \(u\) = initial velocity (49 m/s),
- \(a\) = acceleration (which is \(-g\) or \(-9.8 \, \text{m/s}^2\) since it is acting downwards),
- \(s\) = displacement (which will be \(H/2\) in this case).

3. **Setting Up the Equation**:
- At the maximum height, the final velocity \(v = 0\) m/s. Therefore, we can write:
\[ 0 = (49)^2 + 2(-9.8)(H/2) \]

4. **Rearranging the Equation**:
- Rearranging gives:
\[ 0 = 2401 - 9.8H \]
- This leads to:
\[ 9.8H = 2401 \]

5. **Solving for Maximum Height \(H\)**:
- Dividing both sides by \(9.8\):
\[ H = \frac{2401}{9.8} \]
- Calculating this gives:
\[ H = 245.0 \, \text{m} \]

6. **Finding the Height to Which It Could Further Rise**:
- Since we need to find the height the body could further rise from half the maximum height, we calculate:
\[ \text{Height to rise} = H - \frac{H}{2} = \frac{H}{2} = \frac{245.0}{2} = 122.5 \, \text{m} \]

### Final Answer:
The height to which the body could further rise is \(122.5 \, \text{m}\).

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