Question 48612: Time of flight. 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 elasticity of the pole converts the horizontal speed into vertical speed) Determine how long Johnson was in the air . For how long was he more than 14 ft in the air?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! h= -16t^2 +32t. The elasticity of the pole converts the horizontal speed into vertical speed) Determine how long Johnson was in the air . For how long was he more than 14 ft in the air?
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He will be in the air till his height is zero.
-16t^2+32t=0
-16t(t-2)=0
t=0 or t=2.
He will be in the air for 2 seconds.
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-16t^2+32t=14
-8t^2+16t-7=0
t=[-16+-sqrt(16^2-4(-8)(-7)]/-16
t=[-8+-2sqrt2]
t=0.64644661 or 1.3535534
So, you reach 14 ft. at the smaller time and
you reach it again at the larger time.
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For how long was he more than 14 ft in the air?
larger-smaller is the time you are above 14 ft
1.3535534-0.064644661=1.28890874 seconds.
Cheers,
Stan H.
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