Two Oxford Admissions Questions, Pedulums and Aircraft

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SUMMARY

The discussion focuses on two physics problems related to pendulums and aircraft navigation. The pendulum question involves calculating the period using the formula 2π√(r/10) and understanding the implications of the variable 'r'. The aircraft question requires determining travel time and utilizing trigonometric principles, specifically the cosine rule, to solve for distances traveled at different bearings. The user expresses a need for conceptual clarity rather than exact numerical answers.

PREREQUISITES
  • Understanding of basic physics concepts, specifically pendulum motion.
  • Familiarity with trigonometric functions, particularly sine and cosine.
  • Knowledge of relative motion in the context of aircraft navigation.
  • Ability to interpret and manipulate algebraic equations.
NEXT STEPS
  • Review the physics of pendulum motion and its mathematical derivations.
  • Study the cosine rule and its applications in navigation problems.
  • Practice solving relative motion problems in physics, particularly in aviation contexts.
  • Explore algebraic manipulation techniques to simplify complex equations.
USEFUL FOR

Students preparing for physics exams, educators teaching mechanics, and anyone interested in applying trigonometry to real-world navigation scenarios.

alex3
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Though I'd scan for ease ;)

Homework Statement



Check the Pendulum question out http://dl.getdropbox.com/u/37461/physhelp/secC1.png and http://dl.getdropbox.com/u/37461/physhelp/secC2.png,and the http://dl.getdropbox.com/u/37461/physhelp/secB1.png.

Homework Equations



Should all be in the scans.

The Attempt at a Solution



See the http://dl.getdropbox.com/u/37461/physhelp/workings.png.

Aircraft question: a) seems to be obvious to me; traveling at 170km/h, needs to travel 300km. v = d/t, therefore t = d/v = 300/170 = 30/17 hours (no calculator allowed, left it in a fraction). As for b).. Drew a triangle, due north in an hour he should have traveled 170km, due 010 degrees he traveled 134km, but the question's five marks, and I can't think they expect us to know sin or cos of 10 or 80. The thing that really throws me on this question is that his speed is 'relative to the air'.

Pendulum: Got 2π\sqrt{\frac{r}{10}}, with r being the length of the pedulum. b) I got the same as a), but \frac{r}{15}. I was thrown on these two because the question said 'calculate', so I assume they want an actual integer, but I couldn't find a hint in the question to what r should be to substitute. c) was harder. Could not quite understand the question enough to answer it. d) seemed ok, I ended up with a messy fraction (right at the bottom of the workings scan) and thought I must have buggered up the algebra some where. e) would've probably have been fine if I got d).
I just need pointing in the right direction; it's more getting my head thinking along the right lines than getting the exact integer if required (though that'd be nice!) Thanks!
 
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I'm really sorry for bumping this, I know how irritating it is but I have this test tomorrow, and I know knowing these exact answer won't help for it but I'd like to get my head around the thinking.. :)
 
The aircraft one I have done. Draw a line to show how far he would have traveled in one hour due North, and then the line bearing 10 degrees. Join these two up. You've got two sides and an angle, so cosine rule.

I've done the test now, but I'm still curious about the pendulum one. Any takers?
 

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