A projectile A is projected from ground. An observer B running on ground with uniform velocity of magnitude 'v' observes A to move along a straight line. The time of flight of A as measured by B is T. Then the the range R of projectile on ground is

Options

A. `R=vT`
B. `RltvT`
C. `RgtvT`
D. information insufficient to draw inference

Explanation

To solve the problem, we need to find the range \( R \) of the projectile \( A \) as observed from the ground, given that an observer \( B \) running with a uniform velocity \( v \) sees \( A \) moving in a straight line and measures the time of flight \( T \).

### Step-by-Step Solution:

1. **Understanding the Motion of the Projectile**:
- The projectile \( A \) is launched from the ground with an initial velocity \( u \) at an angle \( \theta \) with respect to the horizontal.
- The horizontal component of the projectile's velocity is given by \( u \cos \theta \).
- The vertical component of the projectile's velocity is given by \( u \sin \theta \).

2. **Time of Flight**:
- The total time of flight \( T \) for the projectile is given by the formula:
\[ T = \frac{2u \sin \theta}{g} \]
where \( g \) is the acceleration due to gravity.

3. **Observer's Perspective**:
- Observer \( B \) is running with a uniform velocity \( v \) and sees the projectile moving in a straight line. For this to happen, the horizontal component of the projectile's velocity must equal the velocity of observer \( B \):
\[ u \cos \theta = v \]

4. **Calculating the Range**:
- The range \( R \) of the projectile on the ground can be calculated using the horizontal component of the velocity and the time of flight:
\[ R = \text{(horizontal velocity)} \times \text{(time of flight)} = (u \cos \theta) \times T \]
- Substituting \( u \cos \theta = v \) into the equation gives:
\[ R = v \times T \]

5. **Final Expression**:
- Thus, the range \( R \) of the projectile as measured from the ground is:
\[ R = vT \]

### Conclusion:
The range \( R \) of the projectile on the ground is given by:
\[ R = vT \]