SATHEE: Kinematics Question 605

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) $t_{1} t_{2} \propto R$

B) $t_{1} t_{2} \propto R^{2}$

C) $t_{1} t_{2} \propto 1 / R$

D) $t_{1} t_{2} \propto 1 / R^{2}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $t_{1} = \frac{2 u \sin θ}{g} and$
$t_{2} = \frac{2 u \sin (90 - θ)}{g} = \frac{2 u \cos θ}{g}$

$∴ t_{1} t_{2} = \frac{4 u^{2} c o s θ \sin θ}{g^{2}} = \frac{2}{g} [\frac{u^{2} \sin 2 θ}{g}]$

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

Hence $t_{1} t_{2} \propto R$

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Kinematics Question 605

Question: A projectile can have the same range R for two angles of projection. If t1 and t2 be the times of flight in two cases, then What is the product of two times of flight?

Options:

Answer:

Solution:

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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?