How do you find the maximum range and height for angles 30 45 and 60?

Answer 1

1. You need to know the velocity of the projectile (V0)

2. The expressions for the range and height assume no air resistance (in vacuum)

3. The units must be consistent e.g. metres and g = 9.81 m/s2

Range in metres for 30 degree launch angle = sin 60 x V02 / 9.81

Range in metres for 45 degree launch angle = sin 90 x V02 / 9.81

Range in metres for 60 degree launch angle = sin 120 x V02 / 9.81

Max. height in metres for 30 degree launch angle = (V0 x sin 30)2 / 2g

Max. height in metres for 45 degree launch angle = (V0 x sin 45)2 / 2g

Max. height in metres for 60 degree launch angle = (V0 x sin 60)2 / 2g

2g is of course 9.81 x 2 = 19.62 m/s2

For interest, at 45 degree launch angle the max. height is 25% of the range.