Question 139842: Use the information from Ex. 115 to determine how long Johnson was in the air. For how long was he more than 14ft in the air?
Ex. 115
For 1989 and 1990 Dave Johnson had the highest decathlon score in the world. When Johnson reached a speed of 32ft/sec on the pole vault runway, his height above the ground t seconds after leaving the ground was given by h=-16t^2 + 32t. (The elasity of the pole converts the horizontal speed into vertical speed.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! to determine how long Johnson was in the air. For how long was he more than 14ft in the air?
Ex. 115
For 1989 and 1990 Dave Johnson had the highest decathlon score in the world. When Johnson reached a speed of 32ft/sec on the pole vault runway, his height above the ground t seconds after leaving the ground was given by h=-16t^2 + 32t.
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h(t) = -16t^2+32t
When he reaches the ground his height is zero.
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-16t^2+32t = 0
-16t(t-2) = 0
t = 2 seconds (time in the air)
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14 ft above the ground?
-16t^2+32t = 14
-16t^2+32t-14 = 0
-8t^2 + 16t-7 = 0
t = [-16 +-sqrt(16^2-4*-8*-7]/-16
t = [-16 +- sqrt(32)]/-16
t = [-16 +-4sqrt(2)]/-16
t = 0.06464466.. or t= 1.3535534..
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These are the two times when he is at 14'
The time he is above 14' is 1.3535534-=0.6464466 = 0.7071 seconds
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Cheers,
Stan H.
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