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If initial height and landing height are the same, the angle of projection that would maximize...

If initial height and landing height are the same, the angle of projection that would maximize horizontal displacement is ______ degrees

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Answer #1

If initial height and landing height are same, vertical displacement is zero.

Place the origin at point of projection, with X axis horizontal and Y axis vertical. Trajectory is in the XY plane.

Let the speed of projection be and angle of projection be .

Horizontal component of velocity is . And Initial vertical velocity is .

Using the equation for vertical motion,

Since vertical displacement is zero,

Hence time of flight is

Horizontal displacement is

is maximum when is maximum. That is or or .

Hence angle of projection for maximum horizontal displacement is

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