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

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) = −4.9t2 + 22t + 6

Answer 1

take the first derivative: -9.8t+22=0 solve for t: t=22/9.8 =or about 2 1/4 seconds or rounded to 3 decimal places, t=2.245 seconds

plug that value into the original equation to find the maximum height, about 30.8 meters

check that by getting the general range for the answer

let t=0 height = 6

t=1 height = -4.9 +22 + 6 = 23.1

t=2 height = -4.9(4)+44+6= 50-19.6=30.4

t=3 height = -4.9(9)+66+6= -44.1+72=27.9

Maximum height is achieved in a little over 2 seconds. 2.245 seconds rounded off

The top of the building is 6 meters high. Maximum height above ground level is 30.8

but that's "just" 24.8 meters above the top of the building.

The original equation has -4.9t² to represent the effect of gravity. It has +22t to represent the initial velocity,upwards. It has the constant term 6 to represent the height of the building.