Help Finding the initial speed as a diver leaves a board.

In summary, the problem involves a diver jumping from a 3.05 m high board with an initial speed of 8.51 m/s and an angle of 75.1 degrees. Using the equation vf^2=vo^2+2a(x), the initial speed of the diver can be determined as 2.79 m/s when the diver makes contact with the water. Basic trigonometry can also be used to solve the problem.
  • #1
DeltaIceman
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0

Homework Statement


A diver springs upward from a board that is 3.05 m above the water. At the instant she contacts the water her speed is 8.51 m/s and her body makes an angle of 75.1 degrees with respect to the horizontal surface of the water. Determine her initial speed as she leaves the board.


Homework Equations


The equations I have to use for this problem were
(Vf^2)=(Vo^2)+2a(x)
x=1/2(Vo+Vf)t
x=(Vo)(t)+1/2(a)(t^2)
Vx=Vo+at
******Note all these equations are interchangable and can be used to find the y components also********

Basic trig functions are also allowed to be used such as cos=x/r and rearranging it to find the values you need. These trig functions also include the pathagorian theroem (sp?)

The Attempt at a Solution


scan0001.jpg


This is all my work that I've done for the equation or at least my last attempt. I tried it a couple different ways but this is the only one I felt like I was getting anywhere. Also The equation I used to get Vo or initial velocity was (Vf^2)=(Vo^2)+2a(x).


I'm sure I'm making a dumb mistake. I went through the rest of the homework problems fairly easy. Then I got to this one and was dumbfounded and decided to seek help elsewhere. I wasn't exactly sure if I could assume the height was 3.05m but I started thinking about the problem and since it states that we want the initial speed as she leaves the board. We could consider that velocity to be almost instantaneous and since the elapsed time is so small that the height was basically 3.05 m. But then again its magnitude is going upward and I wasn't exactly sure how that would through off the height. Anyway If you guys can help me it would be greatly appreciated. I am sorry for any inconvience or any time consumed to help me with this problem. Thank you very much.

~Eric
 
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  • #2
Using your equation [tex]v_{fy}^{2}=v_{0y}^{2}+2ay[/tex] with vf=8.22, a=-9.8 and y=-3.05 yields v0y=2.79m/s. I think you plugged something into your calculator incorrectly because your method is correct (not sure why you got a time value, as it is unneeded).
 
  • #3
Thank you so much. I thought I made a really dumb mistake.
 

Related to Help Finding the initial speed as a diver leaves a board.

1. How is the initial speed of a diver leaving a board determined?

The initial speed of a diver leaving a board is determined by several factors, including the height of the board, the angle of the diver's takeoff, and their body position and technique while in the air. These factors can be measured and calculated using mathematical equations and physical principles.

2. What is the relationship between the height of the board and the initial speed of the diver?

The relationship between the height of the board and the initial speed of the diver is directly proportional. This means that the higher the board, the greater the initial speed of the diver will be. This is because the diver has more potential energy to convert into kinetic energy as they fall from a higher height.

3. How does the angle of the diver's takeoff affect their initial speed?

The angle of the diver's takeoff can greatly affect their initial speed. A more vertical takeoff angle will result in a greater initial speed, while a more horizontal takeoff angle will result in a slower initial speed. This is because a more vertical takeoff allows the diver to convert more of their potential energy into kinetic energy, while a more horizontal takeoff requires the diver to overcome more air resistance.

4. Why is the diver's body position and technique important in determining their initial speed?

The diver's body position and technique play a crucial role in determining their initial speed. A streamlined body position and proper technique can help the diver minimize air resistance and maximize their potential energy, resulting in a higher initial speed. On the other hand, a less efficient body position and technique can lead to a slower initial speed.

5. How does the initial speed of a diver leaving a board affect their dive?

The initial speed of a diver leaving a board can greatly affect their dive. A higher initial speed will result in a longer and more complex dive, as the diver will have more time and energy to perform multiple twists, flips, and other movements. A lower initial speed may limit the diver's ability to perform certain maneuvers and may result in a simpler dive.

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