Aball is thrown downward from a window in a tall building. Its position at time tin seconds is s = 16t ^ 2 + 32t , where s is in feet. How long to the nearest will the ball to fall 276 ?

Step-by-step explanation:

If a ball thrown downward from a window in a tall building is modeled by the equation, s = 16t² + 32t where s in feet, in order to know the time it will take to fall a distance of 276, we will substitute s = 276feet into the equation and calculate for the value of t as shown;

276 = 16t² + 32t

16t² + 32t = 276

Dividing through by 4

4t² + 8t = 69

4t² + 8t - 69 = 0

Using the general formula to find t

t = -b±√b²-4ac/2a

a = 4, b = 8 and c = -69

t = -8±√8²-4(4)(-69)/2(4)

t = -8±√64+1104/8

t = -8±√1168/8

t = -8±34.176/8

t = -8+34.176/8 or -8-34.176/8

t = 3.272 or -5.272

neglecting the negative time, t = 3secs to the nearest seconds

It will take the all 3secs to fall 276 feets