Kinematics: Average Deceleration Underwater

[RedBarchetta]

[SOLVED] Kinematics: Average Deceleration Underwater

Hello! First poster here. Here is a tough question from my online HW:

Homework Statement

A person jumps off a diving board 5.0 m above the water's surface into a deep pool. The person’s downward motion stops 1.6 m below the surface of the water. Estimate the average deceleration (magnitude) of the person while under the water.

Answer: _blank_ m/s^2.

Homework Equations

V^2=Vo^2-2gy
V^2=Vo^2+2a(x-xo)
Vf=0

The Attempt at a Solution

I asked my physics professor for assistance and tried the problem on my own but came to no avail. I started off by using the first V squared formula and plugging in the known variables to find the velocity of the person as they approach the surface of the water.

Then, I plugged the inital velocity into the 2nd V squared equation, as this is the velocity as the person struck the water, and still couldn't find the correct answer. I must be having an algebraic issue.

Okay, there are two distances: 5 m above the water and 1.6 m below the surface of the water. So there is a combined total of 6.6 meters traveled. For above the water:

Vo or inital velocity is zero.

V^2=Vo^2-2gy
V^2=-2gy
V^2=-2(9.8m/s^2)(5m)
V^2=-98m/s

Then take the absolute value of the the square root?

|V|=Sqroot(98m/s)
V=9.8895 m/s

Now, use the second equation to find out the deceleration under the water:

Xo equals zero.
Vf or final velocity is zero.

V^2=Vo^2+2a(X-Xo)
(Plug in inital velocity when the person struck the water and underwater distance for X.)
V^2=(9.8995m/s)^2+2a(1.6m)
V^2=98 m^2/s^2 + (3.2m)a
(Plug in zero for final velocity and move a to the other side)
a=98 m^2/s^2 + 3.2m

Then...? I am not sure. Any help would be great. Thank you!

 

[PhanthomJay]

V^2=(9.8995m/s)^2+2a(1.6m)
V^2=98 m^2/s^2 + (3.2m)a
(Plug in zero for final velocity and move a to the other side)
a=98 m^2/s^2 + 3.2m

Then...? I am not sure. Any help would be great. Thank you!

Welcome aboard! Check your algebra. You have 0 = 98 + 3.2a. You've got to subtract 98 from both sides before you solve for a.

 

[RedBarchetta]

Thank you! That worked. I knew I had a fault somewhere in my Algebra.