Question

Physics students drop a ball from the top of a 100 foot high building and model its height as a function time with the equation h(t) = 100 - 16t^2. Determine, to the nearest tenth of a second, when the ball hits the ground.

Answer 1

When the ball hits the ground, the height is 0.

0 = 100 - 16t²

0 = (10 - 4t)(10 + 4t)

0 = 10 - 4t     or     0 = 10 + 4t

4t = 10          or       -4t = 10

 t = $\frac{10}{4}$             or          t = $-\frac{10}{4}$

Time cannot be negative (unless you have a time machine) so disregard  $-\frac{10}{4}$

Answer: t = $\frac{5}{2}$ = 2.5 seconds