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`TA: Tomoyuki NakayamaMonday, January 24, 2011PHY 2048: Physics 1 with Calculus, Spring 2011 Review: Chapter 3.1-4.7The purpose of this review is to refresh your memory. Physics is a cumulative subject, so make it sure you understand basic concepts and typical problem solving techniques in previous chapters before moving on to a new chapter! ________________________________________________________________________________ A. Vectors In the figure a and b have magnitudes of 4 m and 3 m, respectively. The angles in the figure are 1 = 30º and 2 = 100º. Find the angle and magnitude of the sum of the two vectors.B. Projectile Motion A ball is launched from the base of a ramp with a velocity of magnitude 20.0 m/s at an angle of 45º to the horizontal. The horizontal length of the ramp is d1 = 30.0 m and the height is d2 = 10.0 m. A plateau is located at the top of the ramp. When the ball lands, what is the magnitude of its displacement from the launch point?TA: Tomoyuki NakayamaMonday, January 24, 2011PHY 2048: Physics 1 with Calculus, Spring 2011 Practice Exam Problems (Chapter 3.1-4.7)Working on this problem set is optional, but it is strongly recommended. It is quite possible that some of these problems will appear in the exams. Do it on a weekly basis. Cramming is tiring and sometimes it ends up in a disaster. ________________________________________________________________________________ 1. In the diagram, A has magnitude 12 m and B has magnitude 8 m. The x component of A+B is about (Addition of Vectors) a. 5.5 m b. 7.6 m c. 12 m d. 14 m e. 15 m 2. Let S = (1m)i+(2m)j+(2m)k and T = (3m)i+(4m)k. The angle between these two vectors is given by: (Scalar Product) a. cos-1(14/15) b. cos-1(11/225) c. cos-1(104/225) d. cos-1(11/15) e. cannot be found since S and T do not lie in the same plane. 3. Two vectors lie with their tails at the same point. When the angle between them is increased by 20º the magnitude of their vector product doubles. The original angle between them was about: (Vector Product) a. 0 b. 18º c. 25º d. 45º e. 90º 4. A particle goes from x = -2m, y = 3m, z = 1m to x = 3m, y = -1m, z = 4m. Its displacement is: (Displacement in 3D) a. (1m)i+(2m)j+(5m)k b. (5m)i-(4m)j+(3m)k c. -(5m)i+(4m)j-(3m)k d. -(1m)i-(2m)j-(5m)k e. -(5m)i-(2m)j+(3m)k 5. A ball is thrown horizontally from the top of a 20-m high hill. It strikes the ground at an angle of 45º. With what speed was it thrown? (Projectile Motion) a. 14 m/s b. 20 m/s c 28 m/s d. 32 m/s e. 40 m/s 6. A large cannon is fired from ground level over level ground at an angle of 30º above horizontal. The muzzle speed is 980 m/s. Neglecting air resistance, the projectile will travel what horizontal distance before striking the ground? (Horizontal Range) a. 4.3 km b. 8.5 km c. 43 km d. 85 km e. 170 km 7. A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0 m/s in a vertical circle. Its acceleration at the top of the circle is: (Centripetal Acceleration) a. 9.8 m/s2, up b. 9.8 m/s2, down c. 8.0 m/s2, down d. 32 m/s2, up e. 32 m/s2, down 8. A Ferris wheel with a radius of 8.0 m makes 1 revolution every 10s. When a passenger is at the top, essentially a diameter above the ground, he releases a ball. How far from the point on the ground directly under the release point does the ball land? (Projectile from Circular Motion) a. 0 b. 1.0 m c. 8.0 m d. 9.1 m e. 16 m Answers: 1-c 2- d 3-b 4-b 5-b 6-d 7-e 8-d`

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