Diving Board to Diver's Stopping Point: Solve the Distance

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In summary, a 50 kg diver steps off a diving board and drops straight down into the water, experiencing a net force of 1500 N from the water. The total distance between the diving board and the diver's stopping point under water can be found by comparing the work done on the diver before and after he hits the water. The work done above the water is negative, while the work done below the water is positive. The two work contributions must have the same magnitude, as the diver starts and ends with 0 kinetic energy. Therefore, by setting up and solving equations, the total distance can be found.
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Homework Statement


a 50 kg diver steps off a diving board and drops straight down into the water. The water provides an upward average net force of 1500 N. If the diver comes to rest 5.0m below the water's surface, what is the total distance between the diving board and the diver's stopping point under water?


Homework Equations





The Attempt at a Solution


the total force would be Fn-Fg which is 1500-50*9.81=1009.5N
W=1009.5*(x+5)

i am completely lost on what to do next. please give me a clue or something.
 
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  • #2
princesspriya said:
the total force would be Fn-Fg which is 1500-50*9.81=1009.5N
That's the total force on the diver when he's in the water. What about before he hits the water?
 
  • #3
oo it wud b fg which is 50*9.81 which is 490.5 . but that doesn't help.
 
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  • #4
Sure it helps. There are several ways to solve this kind of problem. One way would be to compare the work done on the diver before he hits the water to the work done on him after he hits the water. After all is said and done, what must the total work (by all forces) be on the diver?
 
  • #5
well you don't know the distance so you cannot find the total work done.
 
  • #6
Think what total work means in reference to his original state (position and velocity) and final state.
 
  • #7
princesspriya said:
well you don't know the distance so you cannot find the total work done.
The distance is what you are asked to find. Try calling the distance from board to water surface D (or whatever). Now set it up and see if you can solve for D. (Then use it to get the total distance.)
 
  • #8
you cannot because you would have two unsolved, the work net and the distance.
 
  • #9
Try it and see. The only unknown is the distance.
 
  • #10
W=1009.5*(x+5) and W=490.5x
are those two equations correct?
 
  • #11
princesspriya said:
W=1009.5*(x+5) and W=490.5x
are those two equations correct?
No.

The diver travels a distance x before hitting the water. What net force acts? What's the net work? Is it positive or negative?

The diver travels 5 m under the water. What net force acts? What's the net work? Is it positive or negative?

What must those two work contributions add to? (Hint: What's the change in KE?)
 
  • #12
well when he is in water the work he does would be 1500N*5m because that's the distance he z traveling and the net force is 1500. so the work done would be 7500J.
The work he does under water would not be the same as above water would it?
 
  • #13
princesspriya said:
well when he is in water the work he does would be 1500N*5m because that's the distance he z traveling and the net force is 1500. so the work done would be 7500J.
1500 N is the force of the water, not the net force. You found the net force in post #1.

The work he does under water would not be the same as above water would it?
Something like that. What are the signs of the two work contributions?
 
  • #14
the work done above water would be negative while the word done below water would be positive. but how can both of them have the same magnitude? that's the part i don't understand.
 
  • #15
princesspriya said:
the work done above water would be negative while the word done below water would be positive.
Just the opposite. Above the water, the work done on the diver is positive: the force (gravity) acts in the same direction as the displacement. Below the water, the net force acts up while the displacement is still down; so the work on the diver is negative.
but how can both of them have the same magnitude? that's the part i don't understand.
Above the water, the diver's KE increases as he falls (since work is being done on him); below the water, it decreases (since negative work is being done on him). It all has to balance out, since he starts with 0 KE and ends up with 0 KE.
 

1. How do you calculate the distance from the diving board to the diver's stopping point?

To calculate the distance, you will need to use the equation d = 1/2 * g * t^2, where d is the distance, g is the acceleration due to gravity (9.8 m/s^2), and t is the time. You will also need to know the initial velocity of the diver, which can be calculated using the equation v = g * t.

2. What is the importance of knowing the distance from the diving board to the diver's stopping point?

Knowing the distance is important for ensuring the safety of the diver. It allows you to properly adjust the height of the diving board and the speed of the diver to ensure they are able to safely reach the stopping point without injury.

3. How does the angle of the diving board affect the distance to the diver's stopping point?

The angle of the diving board affects the distance to the diver's stopping point by changing the initial velocity of the diver. The steeper the angle, the greater the initial velocity and therefore the longer the distance the diver will travel.

4. Can other factors such as wind resistance affect the distance from the diving board to the diver's stopping point?

Yes, other factors such as wind resistance can affect the distance. Wind resistance creates a force that acts in the opposite direction of the diver's motion, which can reduce the distance they are able to travel.

5. How can the calculated distance from the diving board to the diver's stopping point be used in real-life scenarios?

The calculated distance can be used in real-life scenarios to adjust the height of the diving board and the speed of the diver to ensure they are able to safely reach the stopping point. It can also be used to set safety guidelines for diving competitions and to design and test new diving equipment.

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