Two objects are projected with same velocity 'u' at different angles $α$ and $β$ with the horizontal. If $α+β = 90^{\circ}$, the ratio of horizontal range of the first object to the second object will be $[sin(π-θ) = sinθ]$

Question

Two projectiles are projected at $ 30^\circ $ and $ 60^\circ $ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

Answer 1

Step 1: Example
Take $u$ fixed, $\alpha = 30^{\circ}$ and $\beta = 60^{\circ}$. Then $\sin60^{\circ} = \sin120^{\circ} = \frac{\sqrt3}{2}$.

Step 2: Result
The ranges $\frac{u^2}{g}\cdot\frac{\sqrt3}{2}$ are equal. Ratio $1:1$, option (C).

Final Answer:
1:1. \[ \boxed{\text{(C)}\ 1:1} \]

Two objects are projected with same velocity 'u' at different angles \(α\) and \(β\) with the horizontal. If \(α+β = 90^{\circ}\), the ratio of horizontal range of the first object to the second object will be \([sin(π-θ) = sinθ]\)

Show Hint

The Correct Option is C

Solution and Explanation

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