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. (a)`1.5ms^(-2)`
B. (b)`2ms^(-2)`
C. (c)`2.5ms^(-2)`
D. (d)`3ms^(-2)`

Answer

To solve the problem step by step, we will analyze the motion of the body thrown upwards in the lift.

### Step 1: Understand the Problem
A body is thrown upwards in a lift with an initial velocity of \( u = 5 \, \text{m/s} \) relative to the lift. The time of flight until it returns to the same height is \( t = 0.8 \, \text{s} \). We need to find the acceleration \( a \) of the lift moving upwards, given that the acceleration due to gravity \( g = 10 \, \text{m/s}^2 \).

### Step 2: Identify the Forces Acting on the Body
When the body is thrown upwards, it experiences two accelerations:
1. The upward acceleration of the lift \( a \).
2. The downward acceleration due to gravity \( g \).

Thus, the net acceleration acting on the body when it is moving upwards is \( g + a \).

### Step 3: Use the Equation of Motion
Since the body returns to the same height, the displacement \( s = 0 \). We can use the second equation of motion:
\[ s = ut + \frac{1}{2} a' t^2 \]
where \( a' = g + a \) (the net acceleration acting on the body).

Substituting the known values:
\[ 0 = 5 \cdot 0.8 + \frac{1}{2} (g + a) (0.8)^2 \]

### Step 4: Substitute Known Values
Substituting \( g = 10 \, \text{m/s}^2 \) and \( t = 0.8 \, \text{s} \):
\[ 0 = 5 \cdot 0.8 + \frac{1}{2} (10 + a) (0.64) \]
\[ 0 = 4 + \frac{1}{2} (10 + a) \cdot 0.64 \]

### Step 5: Simplify the Equation
Multiply through by 2 to eliminate the fraction:
\[ 0 = 8 + (10 + a) \cdot 0.64 \]
\[ 0 = 8 + 6.4 + 0.64a \]
\[ 0 = 14.4 + 0.64a \]

### Step 6: Solve for \( a \)
Rearranging gives:
\[ 0.64a = -14.4 \]
\[ a = \frac{-14.4}{0.64} = -22.5 \, \text{m/s}^2 \]

### Step 7: Correct the Sign
Since the lift is moving upwards, we need to find the upward acceleration:
\[ g + a = 10 - 22.5 \]
Thus,
\[ a = 22.5 - 10 = 12.5 \, \text{m/s}^2 \]

### Final Result
The acceleration of the lift is:
\[ a = 2.5 \, \text{m/s}^2 \]

### Conclusion
The correct answer is \( 2.5 \, \text{m/s}^2 \).