Chapter 11 QuaDraTiC appliCaTionS 407
5 t − 12 = 0 3t + 1 = 0 (This does not lead to a solution.)
5 t = 12
t = 12
5
= 225
Gary needs 225 hours or 2 hours 24 minutes to unload the truck. John
needs 2 hours 24 minutes + 36 minutes = 3 hours to unload the
truck.
The Height of a Falling Object
We can compute the height of an object dropped, thrown or fired straight
upward with quadratic equations. The general formula is h = −16t^2 + v 0 t + h 0 ,
where h is the object’s height (in feet), t is time (in seconds), h 0 is the object’s
initial height (that is, its height at t = 0 seconds) and v 0 is the object’s initial
velocity (that is, its speed at t = 0 seconds) in feet per second. If the object is
tossed, thrown, or fired upward, v 0 is positive. If the object is thrown down-
ward, v 0 is negative. If the object is dropped, v 0 is zero. The object reaches the
ground when h = 0. (The effect of air resistance is ignored.)
Typical questions are:
When will the object be ____ feet high?
When will the object reach the ground?
What is the object’s height after ____ seconds?
We begin by finding the time it takes for an object to hit the ground after
being dropped, making v 0 = 0 and h = 0.
EXAMPLES
An object is dropped from a height of 1600 feet. How long will it take for
the object to hit the ground?
Because the object is dropped, the initial velocity, v 0 , is zero: v 0 = 0. The
object is dropped from a height of 1600 feet, so h 0 = 1600. The formula
h = −16t^2 + v 0 t + h 0 becomes h = −16t^2 + 1600. The object hits the ground
EXAMPLES
An object is dropped from a height of 1600 feet. How long will it take for
the object to hit the ground?
Because the object is dropped, the initial velocity,
EXAMPLES
An object is dropped from a height of 1600 feet. How long will it take for
