Question

what is the angle of projection of an oblique projectile if its range is u^2/2g

Answer 1

Answer:

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Explanation:

There is a neat formula for the ratio of height to range:

hr=sinθ4cosθ=tanθ4

So whatever angle has a tangent of 4, that’s the angle that sets the ratio of height to range equal to exactly 1.

tan−1(4)=75.96°

Derivation of hr=tanθ4

V = initial velocity of projectile, θ = angle of inclination, g = local gravity

time to reach peak height

t=Vsinθg

height achieved in time t

h=tVsinθ−gt22

Substitute Vsinθg for t :

h=V2sin2θg−V2sin2θ2g

h=V2sin2θ2g

Projectile will be in the air for a total time of 2t .

r=2tVcosθ

Substitute Vsinθg for t :

r=2V2sinθcosθg

Ratio of height to range:

hr=V2sin2θ2g2V2sinθcosθg

Cancel like terms:

hr=sinθ4cosθ=tanθ4