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. $1/R^2$
• B. $1/R$
• C. $R$
• D. $R^2$

Answer 1

Answer: (C)

Range is same for complimentary angles.
$T_{1} = \frac{2u\,sin\,\theta}{g}$ and $T_{2} = \frac{2u\,sin\left(90-\theta\right)}{g}$
and $R = \frac{u^{2}\,sin\,2\theta}{g}$
$\therefore T_{1}T_{2} = \frac{2u\,sin\,\theta}{g} \times \frac{2u\,cos\,\theta}{g} = \frac{2R}{g}$