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Unformatted text preview: Bautista, Aldo Homework 3 Due: Sep 20 2005, 4:00 am Inst: Maxim Tsoi 1 This print-out should have 26 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 3) 10 points Consider the setup of a gun aimed at a target (such as a monkey) as shown in the figure. The target is to be dropped from the point A at t = 0, the same moment as the gun is fired. The bullet hits the target at a point P, which is at the same horizontal level as the gun. Let the initial speed of the bullet be v , let the angle between the vector v and the horizontal ( x-) direction be , and OP= L and AP= h . The gravitational acceleration is g . Denote the time taken to hit the target by T . The acceleration of gravity is 9 . 8 m / s 2 . A P v O This time is given by 1. T = p g h. 2. T = 2 h g . 3. T = s h g . 4. T = s 2 h g . correct 5. T = s h 2 g . 6. T = 3 p g h. 7. T = 2 p g h. Explanation: Basic Concepts: Constant acceleration: x- x = v t + 1 2 at 2 (1) v = v + at (2) Solution: The time T is the time it takes for the monkey to fall from A to P, a distance h . For any object falling a distance h from rest (neglecting air friction), we have from (1):- h = 0 + 1 2 (- g ) T 2 or T = s 2 h g 002 (part 2 of 3) 10 points Find the initial speed v (magnitude of the vector ~ v ) which allows the projectile to meet the target at location P. ( Hint: T defined in part 1 is also the time taken for the bullet to travel, following the projectile trajectory, from O to P). Let the distance OP be L = 2 . 91 m, the angle = 46 . 1 , and the time T = 0 . 785577 s. (Given g = 9 . 8 m / s 2 ). Correct answer: 5 . 34219 m / s. Explanation: We divide v into components: v x = v cos ( * ) v y = v sin The x-velocity is unchanged (there is no hor- izontal acceleration) so we simply use (1) where a = 0 and the bullet is traversing a distance L: L- 0 = v x T + 0 or v x = L/T Now we use ( * ) to find the speed v : v = v x cos = L T cos With the given values we find v = 2 . 91 m . 785577 scos(46 . 1 ) m / s = 5 . 34219 m / s 003 (part 3 of 3) 10 points Bautista, Aldo Homework 3 Due: Sep 20 2005, 4:00 am Inst: Maxim Tsoi 2 Now the same setup is to take place at some planet where the gravitational acceleration is g = g/ 4. Keep v , and h to be the same as before. Find the new height, i.e. the y-coordinate of the new point of collision. ( Hint: you should convince yourself that for this new case, the time taken for the bullet to travel from O to the new point of collision P should still be T ). 1. y = h 4 2. y = h 2 3. y = h 3 4. y = 2 h 5. y = 3 h 4 correct 6. y = 2 h 3 7. y = h 5 8. y = 3 h 5 9. y = h 10. y = 3 h Explanation: If g = g/ 4, we would expect the bullet to hit its target at a higher point, since the target will not fall quite as fast. However, as noted in the hint, the x-motion is still unaccelerated so T will still be the same. So the only...
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This note was uploaded on 10/13/2009 for the course PHY 303K taught by Professor Turner during the Fall '08 term at University of Texas at Austin.
- Fall '08