Question

A baseball pitcher can throw a ball more easily horizontally than vertically. Assume that the pitchers throwing speed varies with elevation angle approximately as v0/2 ​​(1+cosθ0​) where θ0​ is the initial elevation angle and v0​ is the initial velocity when the ball is thrown horizontally.

Find the angle θ0​ at which the ball must be thrown to achieve maximum height.

Answer 1

The ball must be thrown horizontally at an elevation angle of 0 degrees to achieve maximum height.

Step-by-step explanation:

To find the angle θ0​ at which the ball must be thrown to achieve maximum height, we need to determine the elevation angle that gives the highest value for the expression v0/2​​(1+cosθ0​). In this case, v0​ is the initial velocity when the ball is thrown horizontally. To maximize the expression, we need to find the value of θ0​ that maximizes the cosine function.

To find the maximum value of cosθ0​, we know that the cosine function has a maximum value of 1 when θ0​ is 0 degrees. Therefore, the ball must be thrown at an elevation angle of 0 degrees (horizontally) in order to achieve maximum height.