At what angle to the horizon is the ball thrown if it is known that the maximum

At what angle to the horizon is the ball thrown if it is known that the maximum lifting height of the ball is 13 times greater than its flight range?

Data: k – the ratio of the height of the specified ball to the range of its flight (k = 13 p).

To find out the angle of the specified ball, we will use the ratio: k = hmax / lmax = (V0 ^ 2 * sin2α / 2g) / (V02 * sin2α / g) = sin2α / 2sin2α = sin2α / (2 * 2 * sinα * cosα) = sinα / 4cosα = tgα / 4, whence we express: α = arctan 4k.

Let’s calculate: α = arctan 4k = arctan (4 * 13) = arctan 52 = 88º 53’54 ” ≈ 88.9º = 1.5516 rad.

Answer: The ball should have been thrown at an angle of 1.5516 rad to the horizon.