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Question

On lighting a rocket cracker it gets projected in a parabolic path and reaches a maximum height of 4 m when it is 6 m away from the point of projection. Finally it reaches the ground 12 m away from the salting point. Find the angle of projection.

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Solution

The equation of the parabola is of the form x2=4ay
It passes through (6,4)
36=16a a=94
The equation is x2=9y .....(1)
To find the solpe at (6,4)
Differentiating (1) w.r.t x, we get
2x=9dydxdydx=29x
at (6,4), dydx=29×(6)=43
(i.e.,) tanθ=43;θ=tan143
the angle of projection is tan143.

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