a projectile has a maximum range R=150m.find its initial velocity and the corresponding maximum height it reaches. at what angle should it be aimed to hit a target at the same level that is located at a distance x=100m from it?
h max = R/2 = 150m/2 = 75 m.
h max = 0.5g*t^2 = 75
4.9*t^2 = 75
t^2 = 15.31
Tf = 3.91 s. = Fall time.
Tr = Tf = 3.91 s. = Rise time.
V = Vo + g*t = 0 @ max ht.
Vo = -g*t = -(-9.8*3.91) = 38.34 m/s. =
Initial velocity.
R = Vo^2*sin(2A)/g = 100 m.
38.34^2*sin(2A)/9.8 = 100
150*sin(2A) = 100
sin(2A) = 100/150 = 0.66666
2A = 41.8o
A = 41.8/2 = 20.91o