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Unformatted text preview: Version One Homework 4 Heinz 81204 Sep 16, 2004 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. Perpendicular Displacements 04:01, trigonometry, numeric, > 1 min, nor- mal. 001 (part 1 of 1) 10 points Two airplanes leave an airport at the same time. The velocity of the first airplane is 650 m / h at a heading of 40 . The velocity of the second is 550 m / h at a heading of 80 . How far apart are they after 1 . 5 h? Correct answer: 631 . 567 m. Explanation: Under constant velocity, the displacement for each plane in the time t is d = v t. These displacements form two sides of a tri- angle. The angle between the displacements is = 2 r- 1 r . Given two sides, d 1 and d 2 of the triangle and the angle between them, by the law of cosines, the distance between the planes is d = q d 2 1 + d 2 2- 2 d 1 d 2 cos( ) = (975 m) 2 + (825 m) 2- (1 . 23237 10 6 m 2 ) / 1 / 2 = 631 . 567 m . AP B 1993 MC 64 66 04:02, trigonometry, multiple choice, < 1 min, fixed. 002 (part 1 of 3) 4 points A ball is thrown and follows the parabolic path shown. Air friction is negligible. Point Q is the highest point on the path. Points P and R are the same height above the ground. Q R P How do the speeds of the ball at the three points compare? 1. k ~v Q k < k ~v P k = k ~v R k correct 2. k ~v P k < k ~v Q k < k ~v R k 3. k ~v R k < k ~v Q k < k ~v P k 4. k ~v Q k < k ~v R k < k ~v P k 5. k ~v P k = k ~v R k < k ~v Q k Explanation: The speed of the ball in the x-direction is constant. Because of gravitational accelera- tion, the speed in the y-direction goes to zero at point Q . Since points P and R are located at the same point above ground, by symmetry we see that they have the same speed in the y- direction (though they do not have the same velocity). The answer is then v Q < v P = v R . 003 (part 2 of 3) 3 points Which of the following diagrams best indi- cates the direction of the acceleration, if any, on the ball at point R ? 1. correct 2. Version One Homework 4 Heinz 81204 Sep 16, 2004 2 3. 4. 5. 6. 7. 8. 9. The ball is in free-fall and there is no acceleration at any point on its path. Explanation: Since air friction is negligible, the only ac- celeration on the ball after being thrown is that due to gravity. The answer is 004 (part 3 of 3) 3 points Which of the following diagrams best indi- cates the direction of the net force, if any, on the ball at point Q ?...
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