For a given velocity, a projectile has the same range R for two angles of projec

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For a given velocity, a projectile has the same range R for two angles of projection. If t₁ and t₂ are the times of flight in the two cases then

Options:

A . t1t2 α R2

B . t1t2 α R

C . t1t2 α 1R

D . t1t2 α 1R2

Answer: Option B
:
B
For same range angles of projection should be

θ

and 90 -

θ

So, time of flights

t_{1}

=

\frac{2 u s i n θ}{g}

and

t_{2}

=

\frac{2 u s i n (90 - θ)}{g}

=

\frac{2 u c o s θ}{g}

By multiplying =

t_{1} t_{2}

=

\frac{4 u^{2} s i n θ c o s θ}{g^{2}}

t_{1} t_{2}

=

\frac{2}{g}

\frac{(u^{2} s i n 2 θ)}{g}

=

\frac{2 R}{g}

\Rightarrow

t_{1} t_{2}

α

R

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