Two bodies are projected at an angle of ɑ and (90 - θ) to the horizontal with the same speed. The ratio between their time of flight is:
Correct answer: C. Sin θ : cos θ
- A. Cos θ : 1
- B. Sin θ : 1
- C. Sin θ : cos θ
- D. Cos θ : sin θ
- E. Sin θ : tan θ
Explanation
Let the initial velocity be u and the angle of projection be θ.The time of flight for a body projected at an angle θ with the horizontal is given by:T = 2usinθ/gFor the first body projected at an angle θ, the time of flight is:T1 = 2usinθ/gFor the second body projected at an angle (90-θ), the time of flight is:T2 = 2ucosθ/g [ As sin(90-θ)= cosθ ]Taking the ratio of T1 and T2, we get:T1/T2 = (2usinθ/g) / (2ucosθ/g)T1/T2 = sinθ/cosθTherefore, the ratio of time of flight for the two bodies is sinθ: cosθ.
This question appeared on the NUMS 2019 (cancelled sitting) paper, which you can sit online with every answer explained.
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About Projectile Motion
Projectile motion combines uniform horizontal motion with vertically accelerated motion under gravity, assuming air resistance is neglected. Questions use the components of initial velocity to find time of flight, maximum height, horizontal range and position, while distinguishing projectile motion from general circular or one dimensional motion.
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