Question

If two stones A and B are thrown upwards at angles of 30° and 60° respectively with ground at same speed, which stone will have longer horizontal range?

• A. A
• B. B
• C. both A & B will have same range
• D. depend on masses of A and B

Hint:

For projectiles launched with the same speed, the range will be the same for complementary angles \( \theta \) and \( 90^\circ - \theta \).

Answer 1

The Correct Option is C

Step 1: Use the formula for the horizontal range.
The horizontal range \( R \) for 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: Analyze the situation.
Since the velocity is the same for both stones and the only difference is the angle of projection, the horizontal range depends on \( \sin(2\theta) \). For \( \theta = 30^\circ \), \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \), and for \( \theta = 60^\circ \), \( \sin(120^\circ) = \frac{\sqrt{3}}{2} \). Thus, both stones A and B will have the same range.
Step 3: Conclusion.
Thus, both stones A and B will have the same horizontal range, which corresponds to option (C).