A ball is thrown in the air from the top of a building. h (t) = - 4.9t2 + 18t + 7 Its height, in meters above ground, as a function of time, in seconds, is given by h (t) = - 4.9t2 + 18t + 7. How long does it take to reach maximum height? (Round your answer to three decimal places.)

It takes the ball 1.837 s to reach its maximum height.

Explanation:

Hi there!

First, let's write the function h (t):

h (t) = - 4.9 · t² + 18 · t + 7

The velocity of the ball is the variation of height over time, in other words, the velocity is the derivative of the function height with respect to time:

v = dh/dt = - 2 · 4.9 · t + 18 = - 9.8 · t + 18

When the ball reaches its maximum height, its velocity is zero. Then, at the maximum height dh/dt = 0. We can use this to obtain the time it takes the ball to reach the maximum height:

v = - 9.8 · t + 18

0 = - 9.8 · t + 18

-18 / - 9.8 = t

t = 1.837 s

It takes the ball 1.837 s to reach its maximum height.

Have a nice day!