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Question
There are two angles of projection for which the horizontal range of the same. PT the sum of maximum heights for these angles does not depend on the angle of projection.
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Solution
There are two angles of projection for which the horizontal range is same i.e. θ and 90o - θ.
Maximum height H1 for angle projection θ
H1 = (u sin θ)^2/ 2g
Maximum height H2 for angle projection θ
H2 = (u sin(90- θ))^2/ 2g = (u cos θ)^2/ 2g
Now, H1+H2 = (u sin θ)^2/ 2g + (u cos θ)^2/ 2g = u^2 / 2g.
Hence the result.
Maximum height H1 for angle projection θ
H1 = (u sin θ)^2/ 2g
Maximum height H2 for angle projection θ
H2 = (u sin(90- θ))^2/ 2g = (u cos θ)^2/ 2g
Now, H1+H2 = (u sin θ)^2/ 2g + (u cos θ)^2/ 2g = u^2 / 2g.
Hence the result.
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