Math 117

Math 117, Week 8 assignment; 40 points; AACL1085U4 - Laurent

1. (30 points) In 1981, Vadimir Poliakov (USSR) set a world record of 19ft ¾ in for the pole vault (www.polevault.com). To reach that height, Poliakov obtained a speed of approximately 36 feet per second on the runway. The formula h = -16t2 + 36t gives his height t seconds after leaving the ground.

a. Does the graph of this equation open up or down? How did you determine this?

It opens downward because the sign on the t^2 term is negative.

b. Describe what happens to his height as time passes, starting at t=0?

As time passes, starting with t =O, the height of the vault increases until it reaches a peak at 19ft ¾ inches, then the height decreases.

c. Use the method of your choice to find how long he was in the air.

Factoring Method: 0 = -16t^2 + 36t

Factor to remove t: 0 = t (-16t + 36)

Set each term to 0: 0 = t

0 = -16t + 36

16t = 36

t = 36/16 = 9/4

t = 2.25 second, so he was in the air 2.25 seconds.

d. Will his height peak or be at a low during the middle of the time he is in the air? How do you know?

His height will peak during the middle of the time he is in the air since the sign in the t^2 term in the equation is negative.

e. After how many seconds will the peak or low occur?

Factoring Method:

-b/2a

= -36 / (2 * -16)

= -36 / -32

= 36 / 32

= 9 / 8

= 1.125 seconds

f. How high will he be when the peak or low occurs?

Plug in 1.125 seconds:

-16*1.125^2 + 36*1.125

= - 20.25 = 40.25

= 20.25 feet

g. What is the point of the vertex? How does this number relate to your answers in parts e and f?

The vertex is at (1.125, 20.25)

The t coordinate is the time of the peak (1.125).

The h coordinate is the height of the peak (20.25).

h. How many solutions are there to the equation 0 = -16t2 + 36t? How do you know?

The discriminant:

D = b^2 – 4ac

= 36^2 – 4 * -16 * 0

There are two solutions to...