SOLUTION: 1.) you're in a diving competition on the 3m springboard. you hit the water (3m below board) 1.6 seconds after you leave the board. a. what's the initial upward velocity? b.

Question 896373: 1.) you're in a diving competition on the 3m springboard. you hit the water (3m below board) 1.6 seconds after you leave the board.
a. what's the initial upward velocity?
b. when do you pass the board again on the way down?
c. how high above the board did you go?
d. if another person steps off the 10m platform at the same time as you jump for the dive, who hits the water first? how much sooner?
2.) clare can paint a fence in 14 hours. john can paint the same fence in 12 hours. mr smith can paint the fence in 18 hours. if all 3 work together, how long will it take the three people to paint the fence?

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1.) you're in a diving competition on the 3m springboard. you hit the water (3m below board) 1.6 seconds after you leave the board.
You didn't spec a function.
h(t) = -4.9t^2 + vot + h is commonly used with metric units.
a. what's the initial upward velocity?
h(t) = 0 at t = 1.6 seconds
-4.9*1.6^2 + vo*1.6 + 3 = 0
1.6vo = 7.84 - 3 = 4.84
vo = 3.025 m/sec
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b. when do you pass the board again on the way down?
h(t) = -4.9t^2 + vot + h = 3
h(t) = -4.9t^2 + 3.025t + 3 = 3
Solve for t
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c. how high above the board did you go?
h(t) = -4.9t^2 + vot + h is a parabolic function.
Find the vertex
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d. if another person steps off the 10m platform at the same time as you jump for the dive, who hits the water first? how much sooner?
h(t) = -4.9t^2 + 3.025t + 3 = 0 for you.
h(t) = -4.9t^2 + 0t + 3 for the other person.
Solve for t and compare.
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2.) clare can paint a fence in 14 hours. john can paint the same fence in 12 hours. mr smith can paint the fence in 18 hours. if all 3 work together, how long will it take the three people to paint the fence?
In 1 hour, Clare does 1/14, John does 1/12 and Smith does 1/18.
1/t = 1/14 + 1/12 + 18

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