Dave Above Ground
Dave Above Ground
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Word problem?
Decathlon Champion. 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. (The elasticity of the pole converts the horizontal speed into vertical speed.) Find the value of t for which his height was 12 ft.
You don't need to know that he reached a speed of 32ft/sec. That is already in the equation, so you can ignore it.
Substitute 12ft for h and solve for t.
h = -16t^2 + 32t
12 = -16t^2 + 32t
16t^2 - 32t +12 = 0 (divide both sides by 4)
4t^2 - 8t + 3 = 0 (solve for t)
(2t - 3)(2t - 1) = 0
2t =3 or 2t =1
t = 3/2 or 1/2
Since he would be coming down at the later time, he wouldn't have the pole anymore and the formula would not apply. So, the answer should be the shortest time.
1/2 secs
Since 1/2 secs comes first
