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 =
`(10)/(4)` or t =
`-(10)/(4)`

Time cannot be negative (unless you have a time machine) so disregard
`-(10)/(4)`

Answer: t =
`(5)/(2)` = 2.5 seconds