hw4-solutions

# hw4-solutions - bello(rtb473 hw4 Demkov(59910 This...

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bello (rtb473) – hw4 – Demkov – (59910) 1 This print-out should have 51 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Given: The battleship and enemy ships A and B lie along a straight line. Neglect air friction. A battleship simultaneously fires two shells (with the same muzzle velocity) at these two enemy ships. battleship A B If the shells follow the parabolic trajectories shown in the figure, which ship gets hit first? 1. both at the same time 2. A 3. need more information 4. B correct Explanation: The time interval for the entire projectile motion is given by t trip = t rise + t fall = 2 t rise , where t rise is the rising time from 0 to the maximum height, and t fall the falling time from h to 0. In the absence of air resistance t rise = t fall , h = 1 2 g t 2 fall , or t trip = 2 radicalBigg 2 h g . So the smaller is h , the smaller is t trip . In other words, enemy ship B will get hit first. 002 (part 1 of 3) 10.0 points A boy is standing on a cliff. The boy’s hands are a height b above the ground level at the base of the cliff. A monkey is in a tree. The monkey is at a height h above the boy’s hands. At t = 0 the boy throws a coconut upward at a speed v 0 , and at the same time the monkey releases his grip, falling downward to catch the coconut. Assume the initial speed of the monkey is 0 m/s, and the cliff is high enough so that the monkey is able to catch the coconut before hitting the ground. The acceleration of gravity is 10 m / s 2 . b h A ground level B hand height C monkey height v 0 Figure: Consider only vertical motion. How long t does it take for the monkey to reach the coconut? 1. t = 2 v 0 g 2. t = radicalBigg 2 h g 3. t = h v 0 correct 4. t = h 2 v 0 5. t = radicalBigg 2 h g + v 0 g 6. t = v 0 g 7. t = v 0 2 g + h 2 v 0

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bello (rtb473) – hw4 – Demkov – (59910) 2 8. t = radicalBigg 2 h g + h 2 v 0 9. t = v 0 2 g 10. t = 2 h v 0 Explanation: Let y B = 0. The y coordinate of the co- conut as a function of time is y coconut ( t ) = v 0 t 1 2 g t 2 . The y coordinate of the monkey as a function of time is y monkey ( t ) = h 1 2 g t 2 . The monkey is able to catch the coconut when y coconut = y monkey . v 0 t 1 2 g t 2 = h 1 2 g t 2 v 0 t = h , so t = h v 0 . 003 (part 2 of 3) 10.0 points Suppose it takes 2 s for the monkey to catch the coconut and the initial upward speed of the coconut is 5 m / s . Let the y coordinate of the ground, the boy, and the monkey be, respectively, y A = b , y B = 0 , and y C = h . What is the y coordinate of the location where the monkey catches the coconut? 1. y = +15 m 2. y = 5 m 3. y = 20 m 4. y = +2 m 5. y = +8 m 6. y = 10 m correct 7. y = +5 m 8. y = +10 m 9. y = +9 m 10. y = 0 m Explanation: y coconut = v 0 t 1 2 g t 2 = (5 m / s) (2 s) 1 2 (10 m / s 2 ) (2 s) 2 = (10 m) (20 m) = 10 m . 004 (part 3 of 3) 10.0 points Caution: Let upward motion be associated with positive velocity.
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