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

Answer:

After 9 seconds the object reaches ground.

Step-by-step 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

                       $t=\frac{-(-128)\pm \sqrt{(-128)^2-4\times 16\times (-144)}}{2\times 16}\\\\t=\frac{128\pm \sqrt{25600}}{32}\\\\t=\frac{128\pm 160}{32}\\\\t=9s\texttt{ or }t=-1s$

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