Question

A ball is thrown into the air with an upward velocity of 44 ft/s. It’s height h in feet after t seconds is given by the function h=-16t^2 +44t+5. How long does it take the ball to reach its maximum height? What is the balls maximum height?

Answer 1

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Answer:

• 1.375 seconds
• 35.25 feet

Explanation:

A quadratic function y=ax^2 +bx +c is symmetric about the vertical line x=-b/(2a). That is the x-coordinate of the vertex (maximum or minimum).

Here, we have ...

h = -16t^2 +44t +5

t = -44/(2(-16)) = 11/8 = 1.375

It takes 1.375 seconds for the ball to reach its maximum height.

The height at that time is ...

h = (-16(11/8) +44)(11/8) +5 = (-22 +44)(11/8) +5 = 121/4 +5 = 141/4 = 35.25

The maximum height is 35.25 feet.