Rate magnitude of vertical component

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SUMMARY

The discussion centers on calculating the rate at which the vertical component of a skier's trip decreases while moving down a slope of 60 degrees at a speed of 85 km/hr. The term "vertical component" refers specifically to the skier's height relative to sea level. The key takeaway is that the question can be simplified to determining the rate of decrease in height as the skier descends the slope.

PREREQUISITES
  • Understanding of basic trigonometry, specifically sine and cosine functions.
  • Familiarity with concepts of velocity and its components.
  • Knowledge of how to apply derivatives in physics for rate of change calculations.
  • Basic understanding of slopes and angles in physics.
NEXT STEPS
  • Learn how to calculate vertical and horizontal components of velocity using trigonometric functions.
  • Study the application of derivatives in physics to determine rates of change.
  • Explore the concept of slope in physics and its impact on motion.
  • Investigate real-world applications of vertical motion in sports, particularly skiing.
USEFUL FOR

This discussion is beneficial for physics students, sports scientists, and anyone interested in understanding motion dynamics, particularly in relation to skiing and slope navigation.

hulahoop09
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A skier is moving at 85 km/hr straight down a tall mountain having a slope of 60 degrees. At what rate is the magnitude of the vertical component of his trip decreasing?

I just don't understand exactly how to find it. The wording doesn't make sense to me and I don't know where to start.
 
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Hi hulahoop09! Welcome to PF! :smile:
hulahoop09 said:
A skier is moving at 85 km/hr straight down a tall mountain having a slope of 60 degrees. At what rate is the magnitude of the vertical component of his trip decreasing?

The wording doesn't make sense to me …

Yes, it's not the most straightforward way of describing it, is it? :rolleyes:

The "vertical component of his trip" is simply his height (measured vertically, relative to something like sea-level).

"Magnitude" just means "size" … and could just as well have been left out completely!

So the question is really, at what rate is his height decreasing? :smile:
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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