An arrow has an initial launch speed of 39 m/s. If it must strike a target 39 m away at the same elevation, what should be the projection angle?(Hint: sin2θ = 2sinθcosθ)

Answer 1

u = 39 cos T

39 = u t = 39 cos T * t

t = 1/cosT total time in air
rise time = t/2 = 1/(2cosT)

vertical problem
0 = 39 sin T - g * 1/(2 cos T)
but g/2 = 4.9 m/s^2

4.9/cos T = 39 sin T

cos T sin T = 4.9/39

2 sin T cos T = 9.8/39
so
sin 2T = .251
2T = 15.55
T = 7.28 degrees