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This is the only way I can figure out how to show you the diagram.
https://www.google.com/search?q=core+plus+mathematics+course+4&sourceid=ie7&rls=com.microsoft:en-US:IE-Address&ie=&oe=#q=suppose+your+dart+throwing+opponent+is+most+accurate+when+he+throws+at+an+initial+velocity&rls=com.microsoft:en-US:IE-Address
Click on the 3rd link (it should be a PDF). And on the PDF, it is on page 70. (#5).
In the diagram below, a pulley with 5-cm radius is centered at O(0,0). A second pulley with 2-cm radius is centered at B(10,0). The pulley at O is rotating counterclockwise at 2 revolutions per second.
a.) Find the angular velocity of the pulley with center at point B.
Wouldn't both pulleys have the same angular velocity of 2?
b.) Write parametric equations that model the position of point A as the pulley rotates around its center O starting at point (5,0).
I said x=5cos2T and y=5sin2T
c.) Model the position of point C with parametric equations, if its starting position is (12,0).
I said x=2cos2T and y=2sin2T + 10
d.) Enter the algebraic description of both circles, and display the graphs using Simul mode.
e.) Set Tmin and Tmax so that one revolution around the circle with center O is graphed. What happens to the graph of the related motion around the circle with center B? Explain.
I said the graph of the motion of the circle with center B also shows one revolution because it is going at the same speed.
f.) Set Tmin and Tmax so that one revolution around the circle with center B is graphed. What happens to the graph of the related motion around the circle with center O? Explain.
I said the graph of the motion of the circle with center O also shows one revolution because it is going at the same speed.
I wanted to make sure my answers are correct because I have a feeling that they're not because I don't think the answers for e and f should basically be the same...
Many people enjoy the game of darts. there are even national darts tournaments. In one dart game, you stand 8 feet from a dart board and throw three darts per round, attempting to score points totaling 500.
a.) Suppose you are most accurate when you throw a dart at an angle 20° to the horizontal. If the bull's eye is at the same height as your release point, about what initial velocity must you impart to the dart to hit the bull's eye?
b.) How long is the thrown dart in the air?
c.) suppose your dart-throwing opponent is most accurate when he throws at an initial velocity of 30 feet per second. At what angle should he throw his dart to hit the bull's eye?
d.) About how long is his dart in the air?
I was able to solve parts a and b, but I am confused on how to solve for parts c and d. I'm sure once I figure out part c I will be able to figure out part d. Any help would be greatly appreciated! Thanks!
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