How do I find the angle that makes the maximum height equal the range?

Question

The ball is thrown at 51.2 meters per second

Answer 1

Hi Conor,

 

The range R can be found by

 

R = (vo²/g)sin(2θ) where vo is the initial speed and θ is the initial angle of the velocity vector.

 

We can find the maximum height h using the kinematic equation v² = vo² - 2gh. But, at the highest point, v = 0, so

vo² = 2gh. We want h = R. So, vo² = 2gR, or R = vo²/2g, or 2R = vo²/g.

 

Substitute for vo²/g in the horizontal range formula. We then get

 

R = 2Rsin(2θ)

 

Cancel out R. Then we get

 

sin(2θ) = 1/2

 

Or

 

2θ = 30 deg

 

θ = 15 deg

 

The initial speed you gave does not matter. This result is true for all speeds.