The distance travelled by a body during last second of its upward journey is d, when the body is projected with certain velocity vertically up. If the velocity of projection is doubled the distance travelled by the body during the last second of its upward journey is

Options

A. `2d`
B. `4d`
C. `d//2`
D. `d`

Explanation

To solve the problem, we need to analyze the distance traveled by a body during the last second of its upward journey when it is projected with a certain initial velocity.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We are given that the distance traveled by the body during the last second of its upward journey is \( d \).
- We need to find out how this distance changes when the initial velocity of projection is doubled.

2. **Using the Kinematic Equation**:
- The distance traveled during the last second of motion can be calculated using the formula:
\[ d = u + \frac{1}{2} g t^2 - \left( u + \frac{1}{2} g (t-1)^2 \right) \]
- Here, \( u \) is the initial velocity, \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)), and \( t \) is the total time of flight.

3. **Calculating the Time of Flight**:
- The time of flight \( t \) can be calculated using the formula:
\[ t = \frac{2u}{g} \]
- This is derived from the fact that the body will take the same amount of time to go up as it does to come down.

4. **Distance Calculation for the Original Velocity**:
- Substituting \( t \) into the distance formula gives us the distance traveled during the last second:
\[ d = u + \frac{1}{2} g \left( \frac{2u}{g} \right)^2 - \left( u + \frac{1}{2} g \left( \frac{2u}{g} - 1 \right)^2 \right) \]
- Simplifying this expression will yield the distance \( d \).

5. **Doubling the Initial Velocity**:
- Now, if the initial velocity is doubled, i.e., \( u' = 2u \), we need to find the new distance traveled during the last second.
- The new time of flight becomes:
\[ t' = \frac{2(2u)}{g} = \frac{4u}{g} \]
- Using the same distance formula for the last second with this new time \( t' \), we can calculate the new distance \( d' \).

6. **Comparing Distances**:
- Upon calculating \( d' \) using the same method as above, we will find that the distance traveled during the last second when the initial velocity is doubled is still \( d \).
- This is because the distance in the last second of the upward journey does not depend on the initial velocity but rather on the time of flight and the acceleration due to gravity.

### Final Answer:
The distance traveled by the body during the last second of its upward journey when the initial velocity is doubled is still \( d \).