Question

Two bodies of the same mass are projected with the same velocity at an angle \( 30^\circ \) and \( 60^\circ \) respectively. The ratio of their horizontal ranges will be:

• A. 1:1
• B. 1:2
• C. 1:3
• D. \( 2 : \sqrt{3} \)

Hint:

For two projectiles with the same velocity, the horizontal ranges are equal if the angles of projection sum to \( 90^\circ \).

Answer 1

The Correct Option is A

Step 1: Formula for horizontal range.
The horizontal range \( R \) of a projectile is given by the formula: \[ R = \frac{v^2 \sin 2\theta}{g} \] where \( v \) is the velocity, \( \theta \) is the angle of projection, and \( g \) is the acceleration due to gravity.

Step 2: Comparing ranges.
Since the velocities and the acceleration due to gravity are the same for both cases, the horizontal ranges will be the same because: \[ \sin 2 \times 30^\circ = \sin 60^\circ \quad \text{and} \quad \sin 2 \times 60^\circ = \sin 120^\circ \] Thus, the ratio of the horizontal ranges is \( 1 : 1 \).