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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 `20 m//s`. One of them rises 10 m higher than the other. Find the angles of projection. (Take `g= 10 m//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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