Question

A putting green islocated 150 feet horizontally and 50 feet vertically from the tee. What must be the magnitude and direction of the initial velocity if a ball is to strike the green at this location after a time of 2.6 seconds?

Answer 1

g=32.174 ft/s^2
The height of the projectile is
y=h+v sin⁡θ t-1/2 gt^2.
0=50+v sin⁡θ (2.6)-1/2 (32.174) (2.6)^2.
v sin⁡θ=22.60 ft/s.
The horizontal distance to the green:
R=v cos⁡θ t.
v cos⁡θ=R/t=150/2.6= 57.69 ft/s
The initial velocity if a ball is
v=√(〖22.60〗^2+〖57.69〗^2 )=62 ft/s.
The direction is
θ=tan^(-1)⁡〖22.60/57.69〗=21°.