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} $
