Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 413

Finally, we solve height problems for objects that are not dropped. We are
given their initial velocity and height. We are either asked to find the time that
the object will reach a specific height or to find when it will hit the ground.
Because v 0 is not 0, either we will solve the quadratic equation by factoring or
by using the quadratic formula.

EXAMPLE

An object is tossed up in the air from the ground at the rate of 40 feet per

second. How long will it take for the object to hit the ground?

In the formula h = −16t^2 + v 0 t + h 0 , v 0 = 40 and h 0 = 0.

h = −16t^2 + 40t

We want to find t when h = 0.

01640

01640

16 40 00

2

 (  )

(

= –+

=  –+

–+ =

tt

tt

tt= TThisiswhen theobjectistossed

= 

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40  16

40

1

t

66

5

2

25

. 

= 

= 

= 

t

t

t

The object will hit the ground after 2.5 seconds.

A projectile is fired upward from the ground at an initial velocity of 60 feet

per second. When will the projectile be 44 feet above the ground?

In the formula h = −16t^2 + v 0 t + h 0 , v 0 = 60 and h 0 = 0.

h = −16t^2 + 60t

We want to find t when h = 44.

44 = –16t^2 + 60t

16 t^2 – 60t + 44 = 0

EXAMPLE

An object is tossed up in the air from the ground at the rate of 40 feet per

second. How long will it take for the object to hit the ground?

EXAMPLE

An object is tossed up in the air from the ground at the rate of 40 feet per