The horizontal range (R) of a projectile is defined as the horizontal distance it travels while in flight. It is equal to the product of the initial velocity (V) of the projectile, the sine of the angle of projection (θ), and the time of flight (T). R = V * T * sinθ
The maximum height (H) of a projectile is reached at the peak of its trajectory and is equal to the product of half of the gravitational acceleration (g), and the square of the time of flight (T) . H = (1/2) * g * T^2
Given that the horizontal range is equal to three times the maximum height, we can set up the following equation:
R = 3H
We know that R= V * T * sinθ and H = (1/2) * g * T^2
Substituting these equations into the first equation we get:
V* T * sinθ = 3(1/2) * g * T^2
Dividing both sides by T and simplifying, we get:
sinθ = (3/2) * sqrt(g/V)
If we know the value of g (gravitational acceleration) and the initial velocity of the projectile we can calculate the angle of projection. However, in general this is an inverse trigonometric function and the angle of projection is not a exact value, but it is defined in the range of values for the inverse trigonometric functions.
It's important to note that this equation assumes a level ground, no air resistance and constant acceleration due to gravity.