A ball is fired at an angle of 45°, the angle that yields the maximum range in the absence of air resistance. What is the ratio of the ball's maximum height to its range?
A)1.0
B)0.75
C)0.67
D)0.50
E)0.25

Question

Quizplus · Accepted Answer

The maximum height (H) of a projectile is given by $ H = \frac{v^2 \sin^2 \theta}{2g} $ and the range (R) is given by $ R = \frac{v^2 \sin 2\theta}{g} $. For $\theta = 45^\circ$, $\sin 2\theta = 1$ and $\sin^2 \theta = 0.5$. Thus, the ratio $ \frac{H}{R} = \frac{0.5}{2} = 0.25 $.

A Ball Is Fired at an Angle of 45°, the Angle