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Two projectiles are projected at angles ...

Two projectiles are projected at angles `(theta)` and `((pi)/(2)-theta)` to the horizontal respectively with same speed 20m/sec. One of them rises 10m heigher than the other. Find the angles of projection. (Take `g=10m//s^(2)`)

Text Solution

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Maximum height H = `(u^(2)sin ^(2) theta)/( 2 g) rArr h_1 = ((20)^(2) sin ^(2) theta)/(2g) = 20 sin^(2) theta & h_2 = ((20)^(2) sin^(2) (pi//2- theta))/(2g) = 20 cos^(2) theta`
`h_2 - h_1 = 20 [ cos^(2)theta - sin ^(2) theta] = 10 rArr 20 cos 2 theta = 10 rArr cos2 theta = (1)/(2) rArr 2 theta = 60^(@) rArr theta = 30^(@) and theta' = 90^(@) - theta = 60^(@)`
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