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18 days ago

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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?

1 answer:

Ostrovityanka [2.2K]18 days ago

7 0

Answer:

Explanation:

Let us denote the launch angle as $\theta _1=30^{\circ}$ .

$\theta _2=60^{\circ}$ , $\theta _1$ , and $\theta _2$ are complementary angles which means their ranges are identical.

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

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

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

Time of flight is indicated as $=\frac{2u\sin \theta }{g}$ .

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

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

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

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

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

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

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

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