<PRE><B>Question 1063677</B>
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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