For a given initial projectile speed vo, calculate what launch angle a gives the longest range R. Show your work, don t just quote a number.?

NetherCraft 0

1 Answer

  • For a given angle θ from the horizontal:

    Vertical component of velocity will be v.sinθ

    Horizontal component will be v.cosθ

    Time taken to reach maximum height:

    v = u + at

    a = -g

    v = 0

    u = v.sinθ

    0 = v.sinθ – gt

    t = v.sinθ/g

    Distance covered in time t

    = v.cosθ.v.sinθ / g

    = v²sinθcosθ / g

    = v²sin(2θ) / (2g)

    The distance will be maximum when sin(2θ) = 1

    2θ = 90°

    θ = 45°

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