The range R of a projectile is defined as the magnitude of the horizontal displacement of the projectile when it returns to its original altitude. (In other words, the range is the distance between the launch point and the impact point on flat ground.) A projectile is launched at t = 0 with initial speed vi at an angle θ above the horizontal. The range is

Question

R =
vi2sin2θ
g

Use the expression to find the followings.
1. The maximum range of a projectile with launch speed vi.
a)vi^2/2g

b)vi^2/4g

c)4vi^2/g

d)2vi^2/g

e)vi^2/g

(b) The launch angle θ at which the maximum range occurs.

Answer 1

sin of anything is maximum when anything is 90 degrees or pi/2 radians. That maximum is 1.
Then
R = Vi^2/g times one
and 2 theta = 90 so theta = 45 degrees

Answer 2

U2 Sin 2a
= g
=34.66m