# Physics

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a projectile is fired with an initial speed of 53 m/s. Find the angle of projection such that the maximum height of the projectile is equal to its horizontal range

• Physics -

range is v^2 sin(2θ)/g
height is v^2 sin^2(θ)/2g

so,

sin(2θ) = sin^2(θ)/2
2sinθcosθ = sin^2(θ)/2
4cosθ = sinθ
16cos^2(θ) = sin^2(θ) = 1 - cos^2(θ)
17cos^2(θ) = 1
cosθ = 1/√17

• Physics -

0.34 & 0.125

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