The horizontal component of velocity is
Vx = Vcos(37) = 0.7986V ft/s
The vertical component of velocity is
Vy = Vsin(37) = 0.6018V ft/s
The time, t, to reach maximum height is determined by
0 = Vy - gt0 = (0.6018V ft/s) - (32.174 ft/s^2)(t s)
0 = 0.6018V - 32.174t
t = (0.6018V)/32.174 = 0.0187V s
The time to travel 20 ft horizontally takes a time of 2t. Therefore
Vx*(2t) = 20
(0.7986V)*(2*0.0187V) = 20
0.0299V^2 = 20
V^2 = 668.8963
V = 25.86 ft/s
The final velocity will have components (Vx, Vy). Its magnitude will be V or 25.86 ft/s.
V = 25.9 ft/s (nearest tenth)
The given 20 ft in this item is the range of the projectile motion. In dynamics, the equation that relates the range with the initial velocity and the angle is,
Range = (Vo)2sin2θ/g
From the equation, all are given except for the Vo.
Substituting the known values,
20 ft = (Vo)2sin2(37 degress) / 1
The value of Vo is 4.56 ft/s.