Spring Forces-Diving Board question

[Insomniac09]

Hey, I solved this problem but I need someone to double check it. Please and Thank you!

Homework Statement

A 70-kg diver on a springy diving board makes her approach. The diving board sits 1 m above the water below. As she approaches the end of the board she leaps into the air 0.5 meters. She comes down on the board with some speed causing the board to bend. Think of the diving board as a spring with a spring constant of 10,000 N/m. The board then flings her up into the air to some height.

a) To what height above the water does the board send her?

b) What is surprising about your result? What makes it more believable in real life?

Homework Equations

(KE+PEg+PEs)i = (KE+PEg+PEs)F

E=(KE+PEg+PEs) = (.5)mV$$_{2}$$+mgx+(.5)kx$$_{2}$$

x= E/mg

The Attempt at a Solution

I found the distance the board bends:

(KE+PEg+PEs)i = (KE+PEg+PEs)F
0+mg(h+d)+0=0+0+(.5)kd$$_{2}$$
(70)(9.8)(.5+d)=(.5)(10000)d$$_{2}$$
d$$_{2}$$-(.1372)d-(.0686)=0
I used the quadratic formula to get d=0.339m

I found the energy:

E=(KE+PEg+PEs) = (.5)mV$$_{2}$$+mgx+(.5)kx$$_{2}$$
E=0+PEg+PEs)=0+(7)(9.8)(-.339)+(.5)(10000)(-.339)$$_{2}$$
E=(-232.554)+(547.605)=342.051

I found the height:

x= E/mg
x= (342.051)/(70)(9.8)=.4986
.4986+1=1.4986 m

The thing here, is it realistic for her to just have a maximum height of 1.4986m? It seems like all I did was add the 0.5 m that she jumped with the height the board is above the water(1m) but as you can see, I didn't. Thus my question is if 1.4986 is my final answer, it that realistic? And I don't know how I should interpret the b part of the problem. Should my answer be coming out to be an outrageously small or big number? Or is a number around 1.5 the answer I should be getting? Please help because I'm just confusing myself.

 

[Jhero]

Hi there! Great job on solving this problem. I double checked your calculations and they look correct to me. Your final answer of 1.4986m does seem like a reasonable height for the diver to reach after being flung off the board. In real life, there are other factors that may affect the height the diver reaches, such as air resistance and the diver's body position. These factors may make the height slightly different from the calculated value, but overall, your answer seems reasonable and believable. As for the surprising aspect, I believe the fact that the height is not significantly higher than the 1m starting point may be surprising, but as mentioned earlier, there are other factors at play that may affect the final height. Overall, great job on solving this problem and I hope this helps clarify any confusion you may have had. Keep up the good work!