SOLUTION: This is a word problem. #116 Time of flight. Use the information from exercise 115 to determine how long Johnson was in the air. For how long was he more than 14ft in the air. Ex

Question 81936This question is from textbook
: This is a word problem.
#116 Time of flight. Use the information from exercise 115 to determine how long Johnson was in the air. For how long was he more than 14ft in the air.
Exersice 115
For 1989 and 1990 Dave Johnson had the highest decathlon score in the world. When Johnson reached a speed of 32 ft/sec on the pole vault runway, his height above the ground t seconds after leaving the ground was given by h=-16t^2+32t.
How do I solve Problem 116? Please help This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
#116 Time of flight. Use the information from exercise 115 to determine how long Johnson was in the air. For how long was he more than 14ft in the air.
Exercise 115
For 1989 and 1990 Dave Johnson had the highest decathlon score in the world. When Johnson reached a speed of 32 ft/sec on the pole vault runway, his height above the ground t seconds after leaving the ground was given by h=-16t^2+32t.
:
How long he was in the air:
When he returns to the ground, h = 0 (also when he starts h = 0)
:
-16t^2 + 32t = 0
:
Factor out -16t and you have:
-16t(t - 2) = 0
:
The two solutions:
-16t = 0
t = 0/-16
t = 0
and
t = +2 seconds, he was in the air
If you looked at on a graph it would resemble the flight path he takes:
t is on the x axis. Height is on the y axis

:
Notice that t = 0 when he starts and t = 2 when he returns to earth
:
:
For how long was he more than 14ft in the air?
The equation for that:
:
-16t^2 + 32t > 14
-16t^2 + 32t - 14 > 0
:
solve this using the quadratic formula: a=-16, b=32, c=-14
:

:
Do the math here and you should get two solutions:
t > .6464 sec and t < 1.3536 sec
:
We can say he exceeds 14 ft after .6464 sec & went below 14 ft at 1.3436 sec
The problems the problem wants to know how long he was above 14 ft
1.3436 - .6464 = .6972.
:
Let's say .7 seconds, that's roughly what the graph indicates also
:
Did this make sense to you?

RELATED QUESTIONS
Use the information from Ex. 115 to determine how long Johnson was in the air. For how... (answered by stanbon)

Time of flight. For 1989 and 1990 Dave Johnson had the highest decathlon score in the... (answered by stanbon)

I'm not sure what category this word problem would fall into but I picked this one... (answered by ankor@dixie-net.com)

How do I solve this word problem to get my answer. On Monday, there were 24 students... (answered by rfer)

I am having a hard time remembering this stuff from high school and could really use some (answered by nerdybill)

This is a verbal question that has to do with Quadratic Equations. Suppose 5 bales of... (answered by scott8148)

hey guys this is a two part problem not doing so great on I could use your help please. (answered by ankor@dixie-net.com)

Here is the word problem in its exact words. Every year in half moon bay, there is a... (answered by scott8148)

Please help me with this word problem? Britney's flight to Rome leaves New York City... (answered by edjones,checkley71)