Question

If two projectiles are projected with equal velocities at angles which are complementary to each other, then

• A. Heights attained by the projectiles are equal.
• B. The total time of flights are equal.
• C. The range of projectiles are equal.
• D. Their trajectories are equal

Hint:

Compare range, maximum height and time of flight using the standard projectile formulas for angles that add up to 90 degrees.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Take the two angles of projection as \(\theta\) and \(90^{\circ}-\theta\), both with the same speed \(u\).

Step 2: Calculation
Range \(R=\frac{u^{2}\sin 2\theta}{g}\). For \(90^{\circ}-\theta\), \(\sin 2(90^{\circ}-\theta)=\sin(180^{\circ}-2\theta)=\sin 2\theta\), so both ranges are equal.

Step 3: Check the other quantities
Maximum heights are \(\frac{u^{2}\sin^{2}\theta}{2g}\) and \(\frac{u^{2}\cos^{2}\theta}{2g}\). Times of flight are \(\frac{2u\sin\theta}{g}\) and \(\frac{2u\cos\theta}{g}\). These differ unless \(\theta=45^{\circ}\), and the paths differ as well.

Final Answer:
Only the ranges of the two projectiles are equal. \[ \boxed{\text{(C) }\text{The range of projectiles are equal}} \]