Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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1150002     Magnitude and direction of a velocity vector     1150002
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At some instant, you are traveling in your car and your velocity is . What is your speed and what is your direction (unit vector)?

 

1150005     Sketch position and displacement vectors     1150005
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The picture shows a 0.4-kg football after it is thrown. The ball is traveling from left to right in the picture. On the picture, sketch the initial position vector , the final position vector and the displacement vector for the football.


Figure: A football travels left to right.

 

1150004     Displacement; direction cosines     1150004
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A girl walks from the position to the position .

  1. How far is the girl from the origin when she's at ?
  2. What is her displacement?
  3. What is the magnitude and direction of her displacement?
  4. What angle does her displacement make with the x-axis?
  5. What angle does her displacement make with the y-axis?
  6. What angle does her displacement make with the z-axis?

 

1150006     Directon cosines in three dimensions     1150006
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The longest edge of a sail on a sailboat extends from the top of the mast (the origin) to a location . A picture is shown below.


Figure: A sail on a sailboat.

  1. What is the length of the longest edge of the sail (i.e. the length of the hypotenuse of the sail)?
  2. What is the length of the bottom edge of the sail?
  3. What angle does the longest edge of the sail make with the x-axis?
  4. What angle does the longest edge of the sail make with the y-axis?
  5. What angle does the longest edge of the sail make with the z-axis?

 

1150001     Vector sum, magnitude, direction, and angle     1150001
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The following forces act on an object at some instant of time.



  1. What is the sum of the forces (called the net force) on the object at this instant?
  2. What is the magnitude of the net force?
  3. What is the direction of the net force?
  4. What angle does the net force make with the +x axis?
  5. What angle does the net force make with the +y axis?
  6. What angle does the net force make with the +z axis?

 

1150003     Adding position and displacement vectors     1150003
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The initial position of a mouse in a maze is . Its displacement (i.e. change in position) during a time interval of 1 minute is . What is its new position?

 

1180001     Momentum of a toy airplane     1180001
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A 0.020-kg toy airplane is tied to a string which is hung from a ceiling. With the engine turned on, the airplane flies in a horizontal circle. Let's assume that the airplane travels clockwise along the path shown in the figure.


Figure: A toy airplane flying in a circle.

Suppose that the plane's position at s is m, relative to the center of the circle. (A dot is placed at this location in the figure.) A small time interval later, at , the plane's position is m.

  1. Sketch a vector for the initial position (i.e. at s) of the airplane.
  2. Sketch a vector for the final position (i.e. at s) of the airplane.
  3. Sketch a vector for the average velocity of the airplane during this time interval.
  4. What is the average velocity of the airplane during this time interval?
  5. What is the average momentum of the airplane during this time interval?

 

1170004     Position (update) of a fish     1170004
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A graduate student in biology is analyzing video of a school of fish and measures a certain fish to be at the position m moving with a velocity m/s at some instant. Approximately where will the fish be 0.100 s later?

 

1170003     Position (update) of a near-Earth asteroid     1170003
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Near-Earth asteroids are carefully tracked by NASA so that Earthlings will have some notice in the case of a catastrophic collision. You can following the tracking of near-Earth asteroids at

http://neat.jpl.nasa.gov/

Suppose that in a simulation of Asteroid 2007 TU24, it is at the location km relative to the center of Earth with a velocity km/s at some clock reading. What will be its (approximate) position 1 hour later?

Note: Asteroid TU24 made its closest approach to Earth on January 29, 2008. You can read more about it at:

http://www.jpl.nasa.gov/news/news.cfm?release=2008-014a


Figure: According to JPL, "This radar image of 2007 TU24 was obtained on January 28, 2008, about 12 hours before the asteroid's 1.4-lunar-distance pass by the Earth. The Arecibo Observatory in Puerto Rico and the Greenbank Telescope in West Virginia were used to take this image."

 

1170006     Position (update) of Earth     1170006
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At some instant in time, Earth is located at the position m relative to Sun. Its velocity at this instant is m/s in the +y direction.

  1. Where will it be 1 day later?
  2. What assumption did you make in doing this calculation, and is your calculation exact or approximate?

 


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