Question

A projectile can have the same range R for two angles of projection. If $T{­}_{1}and{T}_2$ be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

• A. $R$
• B. $\left(\frac{1}{R}\right)$
• C. $\frac{1}{R^2}$
• D. $R^2$

Answer 1

The correct option is A

$R$

At complementary angles of projection ($\theta$ and ${90}^{\circ }-\theta$), the range is same.
So, $T_1=\frac{2usin\theta }{g}$
and $T_2=\frac{2usin({90}^{\circ }-\theta )}{g}=\frac{2ucos\theta }{g}$
Now, $T_1{T}_2=\frac{4u^{2}sin\theta cos\theta }{g^2}=\frac{2R}{g}$
Hence, $T_1{T}_2\propto R$