SOLUTION: Will someone please show me a completed solution to this word problem. In a diving siblings showcase,11-year-old Hannah takes off from a 24.61 foot platform with an initial v

Question 1063677: Will someone please show me a completed solution to this word problem.
In a diving siblings showcase,11-year-old Hannah takes off from a 24.61 foot platform with an initial velocity of 9.7 feet per second at the same time that her older brother Tyler takes off from a 32.81 foot platform with an initial velocity of 4.51 feet per second. Who enters the water first? By how much? Round to the nearest hundredth.

Thanks very much for your help and your time.
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
since we are working in feet, we use 32 ft/sec/sec to represent acceleration due to gravity
:
h(t) = -(1/2)32t^2 + v(0)t + h(0), where t is time, v(0) is initial velocity, h(0) is initial height and h(t) is height after t seconds
:
Calculate for Hannah, 0 height is when she hits the water
:
0 = -16t^2 + 9.7t + 24.61
:
use quadratic formula to solve for t
:
t = (-9.7 + square root(9.7^2 - 4 * (-16) * 24.61) / (2*(-16)) = -0.97
t = (-9.7 - square root(9.7^2 - 4 * (-16) * 24.61) / (2*(-16)) = 1.58
:
Calculate for Tyler
:
0 = -16t^2 + 4.51t + 32.81
:
t = (-(4.51) + square root((4.51^2) - 4 * (-16) * 32.81) / (2*(-16)) = -1.30
t = (-(4.51) - square root((4.51^2) - 4 * (-16) * 32.81) / (2*(-16)) = 1.58
:
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Hannah and Tyler enter the water at the same time, 1.58 seconds after jumping
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:

Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!
.
In this site, there is a bunch of lessons on a projectile thrown/shot/launched vertically up
    - Problem on a projectile moving vertically up and down
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower
    - Problem on a toy rocket launched vertically up from a tall platform

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".

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