How Fast Must the Boat Travel to Clear the Shark Tank Stunt?

AI Thread Summary
To determine the minimum speed required for the water skier to clear the shark tank, the discussion focuses on the conversion of gravitational potential energy and kinetic energy. The initial gravitational potential energy at the height of the ramp is calculated as U = mgh, while the kinetic energy and work done when the skier is being pulled are expressed as Ef = K + W. The calculations suggest that the skier needs a speed of approximately 7.7 m/s at the base of the ramp to successfully jump over the 5.0-meter-wide tank. There is some confusion regarding the energy calculations needed to clear the distance, particularly how work done against water resistance factors into the overall energy needed. The main question remains about confirming the accuracy of the calculated speed and understanding the energy dynamics involved in the stunt.
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Homework Statement


You've taken a summer job at a water park. In one stunt, a water skier is going to glide up the 2.0-m-high frictionless ramp shown, then sail over a 5.0-m-wide tank filled with hungry sharks. You will be driving the boat that pulls her to the ramp. She'll drop the tow rope at the base of the ramp just as you veer away.
What minimum speed must you have as you reach the ramp in order for her to live to do this again tomorrow?

Homework Equations


U=mgh, K=0.5mv^2, W=Fd

The Attempt at a Solution


when the water skier is standing on the ramp, there is only gravitational potential energy
Ei=U=m*2m*g
then, when I am pull the water skier, there are kinetic energy and work by pulling the water skier
Ef=K+W=0.5mv^2+5F, F=mg because the skier is skiing on water

thus, Ei+Ef= m*g*2=0.5mv^2+5mg= g(h-d)=0.5v^2

I get v=7.7m/s

I am not sure this is the right answer or not.
 
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I don't follow your reasoning - how did you work out the energy needed to get over the 5m distance?
 
Simon Bridge said:
I don't follow your reasoning - how did you work out the energy needed to get over the 5m distance?
while the skier is sailing on water, I think the work on water just equal to mgd.
 
Why?
And what has that got to do with jumping the shark tank?
You are asked for the speed at the bottom of the ramp right?
 
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