Asked by Shay
Robert loves to dive . he joined the diving team . the diving board is feet above the water . if he jumps off the diving board as high as he can ( 10ft/s ) .how high above the water does he get ? and how long is he in mid air before he hits the water ?
Answers
Answered by
PsyDAG
It would help if you proofread your questions before you posted them.
How high is the diving board?
How high is the diving board?
Answered by
Reiny
You have a typo and don't state how high above the water the diving board is.
I will give it an arbitrary value of 6 ft.
So the equation of height is
h = -16t^2 + 10t + 6, where h is in ft and t is in seconds , where t ≥ 0
for a max height, we need the vertex of that parabola
the t of the vertex is -b/(2a) = -10/-32 = .3125 seconds
and the height is -16(.3125^2) + 10(.3125) + 6
= 7.5625 ft
for how long in the air,
You want h = 0
-16t^2 + 10t + 6 = 0
divide by -2
8t^2 - 5t - 3 = 0
Using the formula
t = (5 ± √(25 - 4(8)(-3))/16
= (5 ± √121)/16
= -1/2 or 1
He will be in the air for 1 second
Adjust the above solution to whatever the height of the board is above the water.
I picked the 6 since I knew it would work out nice at the end.
I will give it an arbitrary value of 6 ft.
So the equation of height is
h = -16t^2 + 10t + 6, where h is in ft and t is in seconds , where t ≥ 0
for a max height, we need the vertex of that parabola
the t of the vertex is -b/(2a) = -10/-32 = .3125 seconds
and the height is -16(.3125^2) + 10(.3125) + 6
= 7.5625 ft
for how long in the air,
You want h = 0
-16t^2 + 10t + 6 = 0
divide by -2
8t^2 - 5t - 3 = 0
Using the formula
t = (5 ± √(25 - 4(8)(-3))/16
= (5 ± √121)/16
= -1/2 or 1
He will be in the air for 1 second
Adjust the above solution to whatever the height of the board is above the water.
I picked the 6 since I knew it would work out nice at the end.
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