Question

An object is thrown upward from the top of a 144​-foot building with an initial velocity of 128 feet per second. The height h of the object after t seconds is given by the quadratic equation h equals negative 16 t squared plus 128 t plus 144. When will the object hit the​ ground?

Answer 1

After 9 seconds the object reaches ground.

Explanation:

We equation of motion given as h = -16t²+128t+144,

We need to find in how many seconds will the object hit the ground,

That is we need to find time when h = 0

0 = -16t²+128t+144

16t²-128t-144= 0

`t=(-(-128)\pm √((-128)^2-4* 16* (-144)))/(2* 16)\\\\t=(128\pm √(25600))/(32)\\\\t=(128\pm 160)/(32)\\\\t=9s\texttt{ or }t=-1s`

Negative time is not possible, hence after 9 seconds the object reaches ground.