Question

Three particles A, B and C are projected ground to ground with same speed and at angles 15°, 45° and 75° respectively. Then correct statement is :-

• A. A, B and C have equal range
• B. A, B and C have equal time of flight
• C. C will have maximum range
• D. A and C will have same range

Answer 1

Answer: (D)

A and C will have same range

Answer 2

The range of a projectile is given by $R = \frac{u^2 \sin(2\theta)}{g}$. The range is the same for complementary angles of projection ($\theta$ and $90^\circ - \theta$) because $\sin(2\theta) = \sin(180^\circ - 2\theta)$. Since $15^\circ$ and $75^\circ$ are complementary angles ($15^\circ + 75^\circ = 90^\circ$), particles A and C projected at these angles will have the same range. The maximum range is achieved at $45^\circ$. The time of flight is given by $T = \frac{2u \sin(\theta)}{g}$. For $0^\circ < \theta < 90^\circ$, $\sin(\theta)$ increases with $\theta$. Thus, $15^\circ < 45^\circ < 75^\circ$ implies $T_A < T_B < T_C$. Therefore, A and C will have the same range.