A body is projected vertically up with velocity `98 "ms"^(-1)`. After 2 s if the acceleration due to gravity of earth disappears, the velocity of the body at the end of next 3 s is

Options

A. 49 `"ms"^(-1)`
B. 49.6 `"ms"^(-1)`
C. 78.4 `"ms"^(-1)`
D. 94.7 `"ms"^(-1)`

Answer

To solve the problem, we need to determine the velocity of a body projected vertically upwards after a certain time under the influence of gravity, and then find its velocity when gravity disappears.

### Step-by-Step Solution:

1. **Identify the initial conditions:**
- The initial velocity \( u = 98 \, \text{m/s} \).
- The acceleration due to gravity \( g = 9.8 \, \text{m/s}^2 \).
- The time interval before gravity disappears \( t_1 = 2 \, \text{s} \).

2. **Calculate the velocity after 2 seconds:**
- The formula to calculate the velocity when an object is moving against gravity is:
\[ v = u - g t \]
- Substituting the known values:
\[ v = 98 \, \text{m/s} - (9.8 \, \text{m/s}^2 \times 2 \, \text{s}) \]
- Calculate \( 9.8 \, \text{m/s}^2 \times 2 \, \text{s} = 19.6 \, \text{m/s} \).
- Now, substituting back:
\[ v = 98 \, \text{m/s} - 19.6 \, \text{m/s} = 78.4 \, \text{m/s} \]

3. **Determine the situation after 2 seconds:**
- After 2 seconds, the problem states that the acceleration due to gravity disappears. This means that the body will continue to move with a constant velocity of \( 78.4 \, \text{m/s} \).

4. **Calculate the velocity after the next 3 seconds:**
- Since there is no acceleration acting on the body after 2 seconds, the velocity remains constant.
- Therefore, the velocity at the end of the next 3 seconds is:
\[ v = 78.4 \, \text{m/s} \]

### Final Answer:
The velocity of the body at the end of the next 3 seconds is \( 78.4 \, \text{m/s} \).

---