Minimum Speed for Cliff Diving to Avoid Ledge: What Equation to Use?

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SUMMARY

The discussion focuses on calculating the minimum horizontal speed required for a swimmer to safely clear a ledge while diving off a cliff. The cliff is 9.00 meters high, and the ledge is 1.75 meters wide. To find the initial velocity, participants recommend using the equations of motion for both the vertical (y) and horizontal (x) components. Specifically, the vertical motion equation is set to y = -9, while the horizontal motion equation is set to x = 1.75, allowing for the elimination of time (t) to solve for the initial velocity (v).

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ziddy83
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Ok, here is the question.

A swimmer dives off a cliff with a running horizontal leap. What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom which is 1.75 m wide and 9.00m below the top of the cliff.

which equation would i use? I know the x and y components, but i don't know the time or the initial velocity. can anyone help? Thanks
 
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Yes, you don't know the initial velocity- that's what you are asked to find. You also don't know the time (at which she passes the ledge) so you have two "unknowns". To solve that you need two equations- which you have!

Write out the equation for the height (y component) as a function of time (it's simpler if you take both initial x and initial y as 0). She passes the cliff when she is 9 m below the cliff: set the formula for y = -9. She must be at least 1.75 m from the cliff horizontally: set the formula for x= 1.75. Solve these two equations for v and t.
(The question only asks for v. If you can solve for v by eliminating t, you don't need to then solve for t.)
 
Excellent...thanks.
 

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