Question

A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t) = −4.9t^2 + 12t + 6.

How long does it take to reach maximum height? (Round your answer to three decimal places.)

Answer 1

Explanation:

In order to find out how long it takes the ball to reach its max height, we will find the velocity function (the first derivative of the position function) and then set it equal to 0, since an object at its max height has to stop in the air in order to turn around and come back down. If

`s(t)=-4.9t^2+12t+6`, then the first derivative, the velocity function, is

v(t) = -9.8t + 12 and setting it equal to 0,

0 = -9.8t + 12 and

9.8t = 12 so

t = 1.224 seconds

You could find the max height by subbing the time it takes to reach its max height into the position function:

`s(1.224)=-4.9(1.224)^2+12(1.224)+6` to get that the max height,

s(1.224) = 13.35 meters