JEE MAIN - Physics (2004 - No. 70)
A projectile can have the same range 'R' for two angles of projection. If T1 and T2 be the time
of flights in the two cases, then the product of the two time of flights is directly proportional to
R
$${1 \over R}$$
$${1 \over {{R^2}}}$$
$${R^2}$$
Explanation
Range is same for angle of projection $$\theta ,$$ and $${90^ \circ } - \theta $$
$${T_1} = {{2u\sin \theta } \over g},\,\,{T_2} = {{2u\cos \theta } \over g}$$
$${T_1}{T_2} =$$ $${{4{u^2}\sin \theta \cos \theta } \over {{g^2}}}$$
= $${2 \over g} \times \left( {{{{u^2}\sin 2\theta } \over g}} \right)$$
= $${{2R} \over g}$$
(as $$R = $$$${{{{u^2}\sin 2\theta } \over g}}$$ )
Hence, $${T_1}{T_2}$$ is proportional to $$R.$$