Kinematics Question 605

Question: A projectile can have the same range R for two angles of projection. If $ t _{1} $ and $ t _{2} $ be the times of flight in two cases, then What is the product of two times of flight?

Options:

A) $ {{\text{t}} _{\text{1}}}{{\text{t}} _{\text{2}}}\propto \text{R} $

B)$ {{\text{t}} _{\text{1}}}{{\text{t}} _{\text{2}}} \propto {{R^{2}}} $

C) $ {{\text{t}} _{\text{1}}}{{\text{t}} _{\text{2}}}\propto 1/\text{R} $

D)$ {{\text{t}} _{\text{1}}}{{\text{t}} _{\text{2}}}\propto 1/{{R^{2}}} $

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $ {t _{1}}=\frac{2u\sin \theta }{\text{g}}\text{ and} $
$ {t _{2}}=\frac{2u\sin ( 90-\theta)}{\text{g}}\text{ =}\frac{2u\cos \theta }{\text{g}} $

$ \therefore {t _{1}}{t _{2}}=\frac{4{{u^{2}}}cos\theta \sin \theta }{{{g^{2}}}}=\frac{2}{\text{g}}[ \frac{{{u^{2}}}\sin 2\theta }{\text{g}} ] $

$ =\frac{2}{\text{g}}\text{R,} $ Where R it’s the range.

Hence $ {t _{1}}{t _{2}}\propto \text{R} $



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