Question

The quadratic equation h(t)=-16.1t^2+150 models a balls height,in feet, over time, in seconds, after it is dropped from a 15 story building. How many seconds, rounded to the nearest hundredth, did the ball hit the ground?

Answer 1

$h(t)=-16.1t^{2}+150. \newline\frac{d}{dt}[h(t)=-16.1t^{2}+150] = h'(t) = -\frac{161}{10} \cdot \frac{d}{dt}[t^{2}] + \frac{d}{dt}[150] = 0-\frac{161\cdot2t}{10} = -\frac{161t}{5} = -32.2t \Rightarrow t = 32.2 \ s.$