Question

A bullet is fired with a velocity ‘u’ at an angle ‘θ’ with the horizontal such that it moves under the effect of gravity.

1. What is the nature of its trajectory.

2. Arrive at an expression for time of flight of the bullet.

3. What is the relation between time of ascent and time of decent, when air resistance is neglected.

How the relation is affected when air resistance . is considered.

Answer 1

1. Parabola

2. The time taken by the projectile to cover the horizontal range is called the time of flight.

Time of flight of projectile is decided by usinθ. The time of flight can be found using the formula s = ut + 1/2 at²

Taking vertical displacement s = 0, a = -g and initial vertical velocity = usinθ, we get 

0 = usinθt – 1/2gt²

1/2 gt² = usinθt

t = \(\frac{2usinθ}{g}\).

3. Time of ascent = time of descent

4. Time of descent > time of ascent