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.
2007-09-06 07:09:00 · 4 answers · asked by baby166_99 2 in Science & Mathematics ➔ Mathematics
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
2007-09-06 07:20:20 · answer #1 · answered by Larry C 3 · 1⤊ 0⤋
h = -16t^2 + 32t
12 = -16t^2 + 32t
16t^2 - 32t + 12 = 0
t = 0 when:
[32 +- Sq Rt (1024 - 768)]/32
(32 +- 16)/32
t = 1.5
t = 0.5
2007-09-06 07:30:09 · answer #2 · answered by robertonereo 4 · 0⤊ 1⤋
h = -16t^2 + 32t = 12
4t^2 - 8t + 3 = 0
(2t - 3)(2t - 1) = 0
t = 0.5 and 1.5
2007-09-06 07:24:38 · answer #3 · answered by Beardo 7 · 0⤊ 1⤋
h=12
12=-16t^2+32t
16t^2-32t+12=0
4t^2-8t+3=0
D=8^2-4*4*3
D=64-48
D=16
2007-09-06 07:23:37 · answer #4 · answered by Mario Gomez 3 · 0⤊ 1⤋