SOLUTION: lauren dove into a swimming pool from a 15-foot-high diving board with an intitial upward velocity of 8 feet per second.the equation h(s)= -16s(square root)+8s+15 models the height

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: lauren dove into a swimming pool from a 15-foot-high diving board with an intitial upward velocity of 8 feet per second.the equation h(s)= -16s(square root)+8s+15 models the height      Log On


   

Question 609152: lauren dove into a swimming pool from a 15-foot-high diving board with an intitial upward velocity of 8 feet per second.the equation h(s)= -16s(square root)+8s+15 models the height (H) after (S) after she jumps off the diving board.
i wanna know how to find the time in seconds,it took lauren to enter the water.
also i wanna know what was the greatest height lauren reached when diving?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Lauren dove into a swimming pool from a 15-foot-high diving board with an initial upward velocity of 8 feet per second.
the equation h(s)= -16s^2 + 8s + 15 models the height (H) after (S) after she jumps off the diving board.
:
Everything we need to know is in the equation
-16s^2 = the downward velocity of gravity
+8s = the upward velocity of the diver
15 = height of the diving board
:
The water; h = 0, so we have
-16s^2 + 8s + 15 = 0
you can solve this using the quadratic formula, but this will factor
Multiply by -1
16s^2 - 8s - 15 = 0
(4s - 5)(4s + 3) = 0
positive solution
4s = 5
s = 5%2F4
s = 1.25 seconds to hit the water
:
:
You can confirm this:
h = -16(1.25^2) + 8(1.25) + 15
:
"what was the greatest height Lauren reached when diving?"
use the axis of symmetry formula to find s where the max occurs;
s = %28-8%29%2F%282%2A-16%29
s = %28-8%29%2F%28-32%29
s = .25 seconds
:
Replace s with .25 in the original equation, to find max h
h = -16(.25^2) + 8(.25) + 15