A body is thrown up in a lift with a velocity `5ms^(-1)` relative to the lift and the time of flight is found to be 0.8 s. The acceleration with which the lift is moving up is `(g=10ms^(-2))`

Options

A. `1.5ms^(-2)`
B. `2ms^(-2)`
C. `2.5ms^(-2)`
D. `3ms^(-2)`

Answer

To solve the problem, we need to analyze the motion of a body thrown upwards from a lift that is also moving upwards with an unknown acceleration. We know the following:

- Relative velocity of the body with respect to the lift, \( u = 5 \, \text{m/s} \)
- Time of flight, \( t = 0.8 \, \text{s} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

### Step-by-Step Solution:

1. **Understanding Relative Motion**:
The body is thrown upwards with a velocity of \( 5 \, \text{m/s} \) relative to the lift. If the lift is accelerating upwards with an acceleration \( a \), the effective acceleration acting on the body when it is thrown upwards will be \( g + a \) (since both gravity and the lift's acceleration act in the same direction).

2. **Using the Time of Flight**:
The time of flight \( t \) is the total time the body is in the air before it returns to the same height from which it was thrown. The relative displacement during this time is zero because it returns to the initial position.

3. **Applying the Equation of Motion**:
The equation of motion for the body can be expressed as:
\[ S = ut + \frac{1}{2}(-g - a)t^2 \]
Since the body returns to the same height, \( S = 0 \):
\[ 0 = 5t - \frac{1}{2}(g + a)t^2 \]

4. **Substituting Known Values**:
Substitute \( t = 0.8 \, \text{s} \) and \( g = 10 \, \text{m/s}^2 \):
\[ 0 = 5(0.8) - \frac{1}{2}(10 + a)(0.8^2) \]
Simplifying gives:
\[ 0 = 4 - \frac{1}{2}(10 + a)(0.64) \]
\[ 0 = 4 - (5 + 0.5a)(0.64) \]

5. **Solving for \( a \)**:
Rearranging the equation:
\[ 5 + 0.5a = \frac{4}{0.64} \]
\[ 5 + 0.5a = 6.25 \]
\[ 0.5a = 6.25 - 5 \]
\[ 0.5a = 1.25 \]
\[ a = \frac{1.25}{0.5} = 2.5 \, \text{m/s}^2 \]

### Final Answer:
The acceleration with which the lift is moving upwards is \( a = 2.5 \, \text{m/s}^2 \).