An object is thrown up word from the top of 160 foot building with an initial velocity of 144 ft./s. The height H of the object after T seconds is given by the quadratic equation h= -16t^2 + 144t + 160. When will the object hit the ground?

After 10 seconds

Step-by-step explanation:

In this problem, the height of the object after t seconds is described by the function

where

160 ft is the initial height of the object at t = 0

+144 ft/s is the initial velocity

is the acceleration due to gravity (downward)

Here we want to find the time at which the object hits the ground, so the time t at which

Therefore we can write

Simplifying (dividing each term by 16), we get

This is a second-order equation in the form

Which has solutions given by the formula

(2)

Here we have:

a = -1

b = 9

c = 10

Substituting into (2) we find the solutions:

Which gives:

Since time cannot be negative, the only solution is

t = 10 seconds

28

step-by-step explanation:

because that's the answer