Two projectiles A and B are projected with same speed at angles 15° and 75° respectively to the maximum and have same horizontal range. If h be the maximum height and T total time of flight of a projectile, then

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$h_{A} > h_{B}$

$h_{A} < h_{B}$

$T_{A} < T_{B}$

$T_{A} > T_{B}$

answer is B, C.

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Detailed Solution

$F o r θ_{A} = 15^{0} a n d θ_{B} = 75^{0}, R_{A} = R_{B}$

$U_{A} = U_{B},$

$B u t \frac{h_{A}}{h_{B}} = \frac{u_{A}^{2} \sin^{2} θ_{A}}{u_{A}^{2} \sin^{2} θ_{B}} = {(\frac{\sin 15^{0}}{\sin 75^{0}})}^{2} < 1$

$o r h_{A} < h_{B}$

$A g a i n, \frac{T_{A}}{T_{B}} = \frac{u_{A} \sin θ_{A}}{u_{B} \sin θ_{B}}$

$= \frac{\sin 15^{0}}{\sin 75^{0}} < 1$

$o r T_{A} < T_{B}$

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