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Unformatted text preview: Dr. Galeazzi PHY205 Test #1 February 14, 2010 Signature: ___________________________ I.D. number: _________________________ Name:_______________________________ 1 You must do the first problem which consists of five multiple choice questions. Then you can skip one of the four long problems numbered 25. Clearly cross out the page and the numbered box of the problem omitted. Do not write in the other boxes. If you do all the problems, only problems 14 will be graded. Each problem is worth 25 points for a total of 100 points. TO GET CREDIT IN PROBLEMS 2  5 YOU MUST SHOW GOOD WORK. 2 3 4 CHECK DISCUSSION SECTION ATTENDED: 5 [ ] Dr. Nepomechie 2O, 9:30 10:20 a.m. [ ] Dr. Voss 2Q, 12:30 1:20 p.m. [ ] Dr. Voss 2R, 2:00 2:50 p.m. [ ] Dr. Huffenberger 2S, 3:30 4:20 p.m. [ ] Dr. Galeazzi 4P, 11:00 11:50 a.m. TOTAL EQUATION SHEET (Make sure to start all problems from these equations only) Vectors: Linear motion: 2D: , ; ; Relative velocity:
/ / / ; tan ; ; ; cos , ; sin . ; / / 1 Dr. Galeazzi [1.] PHY205 Test #1 February 14, 2010 This problem has five multiple choice questions. Circle the best answer in each case. [1A.] An average car runs for about 250,000 km. How many inches is that? (Remember that 1 inch~2.5 cm). 2.5 [1B.] If 31. 10 4.0 and 6. 10 25. 8.0 10 1 2.5 10 . 6. 8.0 10. 4.0 , find , [1C.] The magnitude of the gravitational force between two planets is given by where and are the masses of the two planets, r is the distance between them, and the force has units of a mass times an acceleration. What are the SI units of G? [1D.] If Find the value of , with for 3.50 , 2.00 . 2 2.00 2 3.50 4.000 14.0 4.00 10.0 6.0 2.00 4.000 2.50 4.000 , 14.0 , and 2.50 . (both with [1E.] A river runs downhill with speed . A boat crosses the river with speed respect to the river), making an angle uphill to the perpendicular to the river (see Figure). What is the speed of the boat with respect to the ground?
cos sin 2 sin 2 Dr. Galeazzi PHY205 Test #1 February 14, 2010 [2.] Two cars, an Acura and a Bentley, are initially at rest a distance L from each other. At time 0 both cars starts accelerating toward each other with constant acceleration and respectively. a) b) c) At what time does the crash happen? Find the distance traveled by the Bentley before the two cars crash into each other. What is the relative speed of the Bentley, with respect to the Acura, just before the crash? Write your results in terms of L, , and . Remember to check the dimensions/units for each answer. Set the axes with the origin at the initial position of the Bentley, and the positive xaxis pointing toward the Acura. The equations of motion for each care therefore are: Acura: , 0, Bentley: , 0, 0 1 2 2 1 2 a) The cars crash when they are in the same place at the same time: Check units: 1 2 1 2 1 2 b) Since the Bentley is initially in the origin, the distance traveled is just the coordinate of the crash: 1 1 2 2 2 Check units: c) Just before the crash , Check units:     2 3 Dr. Galeazzi PHY205 Test #1 February 14, 2010 [3.] Using a reference frame with the origin at the takeoff airport, the positive xaxis due East, and the positive yaxis due North, the acceleration of an airplane as a function of time can be described as: , with , , and positive and constant. Assuming that the airplane takes off from the airport at time 0 with zero initial velocity: a) What are the units of , , and ? b) Find the time(s) when the airplane position is directly NE of the airport. c) Find the trajectory of the plane, y(x). Write your results in terms of , , and . Remember to check the dimensions/units for each answer. a) b) X: , 0, ; 0 Y: , 0, NE implies that 0 1 5 Check units: c) Check units: 0 5 1 5 1 2 0 1 2 1 2 1 6 1 5 1 30 ; . 1 2 ; 1 6 . 4 Dr. Galeazzi PHY205 Test #1 February 14, 2010 [4.] A cannon is placed on a tower an UNKNOWN height h from the ground. The cannon is inclined an angle from the horizontal when a ball is fired. Assuming that there is no friction, that the initial speed of the ball is , and that the ball lands a distance L from the base of the tower: a) How high above ground does the ball go? b) What is the speed of the ball at the maximum height? c) What is the height h of the tower? If needed, you can assume you know h for parts (a) and (b). Write your results in terms of , , L, g, and h (only for parts a and b). Remember to check the dimensions/units for each answer. a) Set the origin at the base of the tower. x: y: 0, , cos , sin , sin 0 sin sin 0, therefore 0, and 1 2 1 2 cos cos sin cos sin cos cos sin 0 cos sin 1 2 sin cos sin The maximum height is given for Check units: b) At the maximum height Check units: 1 2 c) The ball hits the ground when cos 0 Check units: 5 Dr. Galeazzi PHY205 Test #1 February 14, 2010 [5.] A particle is free to move along the xaxis. The particle is subject to a negative acceleration 12 , and at time 1 is at 14 moving proportional to time with velocity 10 / . a) Find the time(s) when the particle passes through the origin; b) Find the velocity(ies) of the particle when it passes through in the origin. Let's write , with 12 . 1 2 Using the initial condition: 1 12 1 10 6 16 10 2 Moreover: 1 1 2 6 Using the initial condition: 1 12 1 16 1 50 6 14 2 16 0 1 . 6
a) Find t for 0: 1 6 6
, 0, 0, 6 16 12 8 22 NOTE: It is OK to discard the negative solution. b) 16 1 2 6 3 2 32 , 6 ...
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This note was uploaded on 01/08/2012 for the course PHYSICS 205 taught by Professor Galeazzi during the Fall '11 term at University of Miami.
 Fall '11
 Galeazzi

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