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.?

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°