Physics Two Dimensional Motion Question 153
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}} $
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Answer:
Correct Answer: A
Solution:
[a] $ {t _{1}}=\frac{2,u,,\sin \theta }{\text{g}}\text{ and} $
$ {t _{2}}=\frac{2,u,,\sin ( 90-\theta)}{\text{g}}\text{ =}\frac{2,u,,\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 is the range. Hence $ {t _{1}}{t _{2}}\propto \text{R} $
BETA
