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 last second of its upward journey is

Options

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

Answer

To solve the problem, we need to analyze the motion of a body projected vertically upward and determine how the distance traveled during the last second of its upward journey changes when the initial velocity is doubled.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Let the initial velocity of projection be \( u \).
- The distance traveled during the last second of the upward journey is given as \( d \).

2. **Time of Flight**:
- The time of flight \( T \) for a body projected upwards with initial velocity \( u \) can be calculated using the formula:
\[ T = \frac{2u}{g} \]
where \( g \) is the acceleration due to gravity.

3. **Distance Traveled in the Last Second**:
- The distance traveled during the last second of the upward journey can be calculated using the formula:
\[ d = u - \frac{g}{2} \quad \text{(for the last second)} \]
- This formula represents the distance covered in the last second of the upward journey.

4. **Doubling the Initial Velocity**:
- If the initial velocity is doubled, the new initial velocity becomes \( 2u \).
- The new time of flight \( T' \) is:
\[ T' = \frac{2(2u)}{g} = \frac{4u}{g} \]

5. **Distance Traveled in the Last Second with New Velocity**:
- The distance traveled during the last second of the upward journey with the new initial velocity \( 2u \) can be calculated as:
\[ d' = 2u - \frac{g}{2} \]

6. **Comparing Distances**:
- We can express \( d' \) in terms of \( d \):
\[ d' = 2u - \frac{g}{2} = 2\left(u - \frac{g}{2}\right) = 2d \]
- Therefore, when the initial velocity is doubled, the distance traveled during the last second of the upward journey becomes \( 2d \).

### Final Answer:
The distance traveled by the body during the last second of its upward journey when the velocity of projection is doubled is \( 2d \).