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 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?
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For projectiles with the same range, the product of the times of flight is proportional to the square of the range.
Updated On: Mar 25, 2026
- \( t_1 t_2 \propto R \)
- \( t_1 t_2 \propto R^2 \)
- \( t_1 t_2 \propto R^3 \)
- \( t_1 t_2 \propto R^4 \)
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The Correct Option is B
Solution and Explanation
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).
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