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.
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