Question

A basketball player throws the ball at different angles. At which of 

 the following angles will the ball achieve the maximum height when 

 the initial velocity given is the same for all the angles?

Answer 1

Write the equation for the height of a ball thrown at some angle above the horizontal:

$$h=\frac{v^2\sin^2\theta}{2g}.$$

The maximum value of h is when the sine is 1, or when the angle is 90° from the horizontal.