Question

Two projectiles are launched with the same initial speed from the same location, one at a 30° angle and the other at a 60° angle with the horizontal. They land at the same height at which they were launched. If air resistance is negligible, how do the projectiles’ respective maximum heights, H30 and H60 , and times in the air, T30 and T60 , compare with each other?

Answer 1

Answer:

Explanation:

Given

launch angle $\theta _1=30^{\circ}$

$\theta _2=60^{\circ}$

$\theta _1$ and $\theta _2$ are complimentary angles so range for both of them is same

$H_{max}=\frac{u^2(\sin \theta )^2}{2g}$

$H_{30}=\frac{u^2(\sin 30)^2}{2g}$

$H_{30}=\frac{u^2}{8g}$

time of flight $=\frac{2u\sin \theta }{g}$

$t_{30}=\frac{u}{g}$

For $\theta =60^{\circ}$

$H_{60}=\frac{u^2(\sin 60)^2}{2g}$

$H_{60}=\frac{3u^2}{8g}$

$t_{60}=\frac{2u\sin 60}{g}=\frac{\sqrt{3}u}{g}$

$H_{60}=3\times H_{30}$

$t_{60}=\sqrt{3}\times t_{30}$