Answer:
Explanation:
In projectile,
Maximum height = [tex]\frac{u^{2}sin^{2} \theta }{2g}[/tex] and range = [tex]\frac{u^{2}sin2\theta }{g}[/tex]
u = velocity of the body
[tex]\theta[/tex] = angle of launch
g = acceleration due to gravity
If the range equals the maximum height in an ideal projectile launch on a horizontal plane, this means;
[tex]\frac{u^{2}sin^{2} \theta }{2g} = \frac{u^{2}sin2\theta }{g}[/tex]
since [tex]sin2\theta = 2sin\theta cos\theta[/tex]
[tex]\frac{u^{2}sin^{2} \theta }{2g} = \frac{u^{2}2sin\theta cos\theta }{g}\\\frac{sin\theta}{2} =2cos\theta \\sin\theta = 4cos\theta\\\frac{sin\theta}{cos\theta} = 4\\tan\theta = 4\\\theta = tan^{-1} \\4\theta = 75.9^{0}[/tex]
The angle at which the range equals the maximum height in an ideal projectile launch on a horizontal plane is approximately 76°
