The ratio of maximum height of projectile is 4.determine the angle of projection?

To determine the angle of projection for a projectile when the ratio of its maximum height to its range is 4, we can use the following formula:

Ratio of maximum height to range = tan^2(angle of projection)

Let's denote the angle of projection as θ.

Given that the ratio of maximum height to range is 4, we can write the equation as:

4 = tan^2(θ)

To find θ, we need to take the square root of both sides of the equation:

√4 = √tan^2(θ)2 = tan(θ)

Now, we can find the angle of projection θ by taking the inverse tangent (arctan) of both sides:

θ = arctan(2)

Using a calculator or trigonometric tables, we find that the angle of projection is approximately 63.43 degrees.

Therefore, the angle of projection for a projectile with a maximum height-to-range ratio of 4 is approximately 63.43 degrees.