Question

A potato is launched into the air at a velocity of 60 feet per second off of a building that is 210 feet tall. This can be modeled by the formula h=-16t^(2)+60t+210, where h is the height (in feet) after t seconds. When will the potato hit the ground? (Round to the nearest second.)

Answer 1

The equation models the height of a projectile in feet above ground (h=0) with g=-32 ft/s^2 at a height of 210 ft. with an initial velocity (upwards) of 60 ft/s.

The time it takes to reach the ground can be obtained by solving the equation h(t)=0.

h(t)=0 =>
-16t^2+60t+210=0
=>
16t^2-60t-210=0
Solve by completing the square:
t^2-(60/16)t-210/16=0
=>
(t-60/32)^2=(60/32)^2-210/16
Simplify
t-15/8= ± sqrt(1065)/8
=>
t=15/8 ± sqrt(1065)/8
=-2.20 s. or 5.95 seconds  (to two decimals).

Answer: after 5.95 seconds, the potato will hit the ground, assuming no air resistance.