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Posted 07 March 2008 - 07:50 PM
Jeff, Yes the forward force decreases, but the total force increases - as the skier is using the increased drag to accelerate him 'sideways'. Once he is moving forwards and sideways, his total velocity can be calculated with Pythagoras and can be easily seen to be higher that the boats simple forward speed. You need a paradigm shift in your thinking - how about yachts? do you understand how a yacht sails into the wind?
Letâ€™s presume that increased drag slows the boat down. That means that the pulling force via the rope decreases. I still canot understand why the waterskier accelerates when the waterskier moves at an angle relative to the direction of the boat.
I cannot understand your point. What causes the skier to accelerate when angling away from the center line of travel?
Posted 07 March 2008 - 08:24 PM
No - the acceleration is when the skier is angling away from the boat. His forward velocity is decreasing (along with the boat), but his sideways velocity is increasing at a much higher rate. His total velocity is the sum of his sideways and forward velocities. (pythagoras) When the skier turns back toward the boats direction of travel, the tow rope goes slack and the skier starts to decrease total velocity - but most of his sideways velocity has been converted into forward velocity. As soon as he turns, his new forward velocity is greater than the boats.
Jeff, it is when the skier is angling back towards the centerline that they are accelerated.
Posted 07 March 2008 - 08:37 PM
Posted 07 March 2008 - 08:47 PM
Posted 07 March 2008 - 10:03 PM
Speed does not have a direction, velocity and acceleration do. Driving in circles at constant speed you have a constant speed but the velocity is changing all the time due to a constant acceleration towards the middle of the circle. Just remember any time something changes speed or direction it has accelerated.
I cannot understand why the car is accelerating if it travels at a constant speed.
Posted 08 March 2008 - 12:30 AM
Jeff, I think I was incorrect when I stated that. I believe the skier would be able to accelerate whether they were moving towards or away from the centerline as they are able to generate a force on the tow rope in either direction, and that force is what causes the acceleration.
Thanks for the reference.
You also state that the waterskier accelerates when he comes back to the centerline. Are you sure? I though that acceleration happens when he moves away from the centerline â€“ because the tow rope has a â€œfixedâ€ length and if the tow rope attached to the boat moves forward at a constant speed, and the skier is moving sideways away from the center + also moving forward at the same speed as the boat, the skier must be traveling a greater distance per unit time, and therefore must be traveling faster.
Posted 08 March 2008 - 02:15 AM
Matt â€“ can you refer me to a Pythagoran equation that discusses speed rather than the relationship between side lengths in a triangle?I can't refer you anywhere, to me they're the same thing - but speed/velocity just has a time variable on both sides of the equation. This is probably hard if you don't have high school physics. How about this, picture a remote control hovercraft on an ice rink (low friction) 2 fan blowers on the hovercraft, the main fan at the back can propel it forward at a maximum speed of 20kph. A smaller thruster fan on the side of the hovercraft can propel it sideways at 5kph. If both fans are operating at full force, the hovercraft is moving at the square root of 20 squared plus 5 squared which is equivalent to the square root of 425 = 20.61kph
Posted 08 March 2008 - 02:33 AM
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