Question

A projectile can have the same range \( R \) for two angles of projection. If \( t_1 \) and \( t_2 \) are the times of flight in two cases, then what is the product of two times of flight?

• A. \( t_1 t_2 \propto R \)
• B. \( t_1 t_2 \propto R^2 \)
• C. \( t_1 t_2 \propto R^3 \)
• D. \( t_1 t_2 \propto R^4 \)

Hint:

For projectiles with the same range, the product of the times of flight is proportional to the square of the range.

Answer 1

The Correct Option is B

Step 1: Relation between time of flight and range.
For a projectile, the time of flight \( t \) and range \( R \) are related by the equation: \[ R = \frac{v^2 \sin(2\theta)}{g} \] where \( v \) is the initial velocity, \( \theta \) is the angle of projection, and \( g \) is the acceleration due to gravity.

Step 2: Product of the times of flight.
The times of flight for two angles giving the same range are related by: \[ t_1 t_2 \propto R^2 \] Thus, the correct answer is (2).