MI Practice Test Solutions

MI Practice Test Solutions - Question (1150002) Magnitude...

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Unformatted text preview: Question (1150002) Magnitude and direction of a velocity vector At some instant, you are traveling in your car and your velocity is h 30 , , 20 i m / s . What is your speed and what is your direction (unit vector)? Solution ~v = < 30 , , 20 > m / s | ~v | = p (30) 2 + 0 2 + (20) 2 m / s = 1300 m / s = 36 m / s v = ~v | ~v | = < 30 , , 20 > m / s 36 m / s = < . 83 , , . 56 > m / s Question (1150003) Adding position and displacement vectors The initial position of a mouse in a maze is h . 2 , , . 6 i m . Its displacement (i.e. change in position ) during a time interval of 1 minute is h- . 5 , , . 3 i m . What is its new position? Solution Restate the question in terms of variables. initial position: ~ r i = < . 2 , , . 6 > m displacement: ~ r = <- . 5 , , . 3 > m nal position: ~ r f = ? m Sketch a picture of the situation. Figure 1: The initial position, displacement, and nal position of a mouse. The de nition of displacement is change of position" or ~ r = ~ r f- ~ r i To get the mouse's new position, take its initial position and add its displacement. ~ r f = ~ r i + ~ r Substituting for the variables gives: ~ r f = ~ r i + ~ r ~ r f = < . 2 , , . 6 > m+ <- . 5 , , . 3 > m ~ r f = <- . 3 , , . 9 > m Compare this answer to the vector shown in the picture. They are consistent, thus giving one con dence that it the answer is probably correct. Question (1130001) Linear interaction(s); three di erent hockey pucks You view the motion of a hockey puck in a video and mark its location every 0.2 s. The resulting motion map for three di erent hockey pucks is shown below. The hockey puck in each case is moving to the right. Figure 1: A hockey puck travels to the right in three di erent cases. In which case (A, B, or C) is there no interaction between the hockey puck and its surroundings? (Or rather, no net interaction .) If there is no interaction in all or none of the cases, then state so. Explain your reasoning. Solution Puck B. According to Newton's rst law, an object moves in a straight line and at a constant speed except to the extent that it interacts with other objects. In other words, if it does not interact with other objects, then it will have a constant velocity (a constant speed and a constant direction). From the motion diagrams, it can be seen that puck A is speeding up, puck B is moving at a constant speed, and puck C is slowing down. (Note: they are all moving to the right.) Because puck B moves in a straight line at a constant speed, it is not interacting with its surroundings. Question (1150006) Directon cosines in three dimensions The longest edge of a sail on a sailboat extends from the top of the mast (the origin) to a location h- 2 . ,- 4 . , 1 . 5 i m . A picture is shown below....
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This note was uploaded on 05/02/2011 for the course GE 208K taught by Professor Dutt during the Spring '11 term at University of Texas at Austin.

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MI Practice Test Solutions - Question (1150002) Magnitude...

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