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Vectors Problem Packet Homework Solutions (1-14)

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7. A man walks 9 km east and then 15 km west. Find his distance traveled and his displacement. dd 9 km [E] 15 km [W] d = 6 km [W] Distance = 9 km + 15 km = 24 km Added the vectors tip-to-tail Scalar: No direction Vector: direction and “little hat” Resultant is d

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R 100 mi/h 40 mi/h = v 9. A robin is flying south for the winter at a rate of 40 miles per hour when it runs into a hurricane blowing due west at 100 miles per hour. What is the new velocity of the robin? Find the resultant, which is the new velocity. Obviously, the robin was sped up by the hurricane!!!

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R 90 lbs [W] 210 lbs [Down] = F 10. Tarzan is hanging from one of his vines. His weight (his force) is 210 pounds, directed Southwards (actually, downward would be more appropriate). A boy sees that Tarzan wants to be pushed on his vine. The boy pushes with a force of 90 pounds West. The rope can withstand a 225-lb force. What happens to the “King of the Apes”? (Find both the magnitude and the direction of the resultant). Find the resultant, which is the force in the vine. Since 228.5 lbs is greater than what the rope can take (225 lbs), Tarzan will fall!

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R Worp 8 [E] Worp 4 [N] 11. The world is again being attacked by hostile aliens from outer space. This looks like a job for Superman! With his super strength, he is able to fend off the attack. However, he wants to rid the earth of these dangerous aliens forever. As they fly away, they must pass close to our sun. They are heading on a bearing of East with a speed of Worp 8. If Superman can change their course to a bearing of between [N 61 o E] and [N 64 o E], they will crash into the sun. He gives them a velocity of Worp 4 on a bearing North. What happens? Has Good triumphed again? Since 61 < 63.4 < 64 o, the world is safe!!!!! or ….

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R 2500 N 1000 N = F 12. On a television sports review show, a film clip is shown of the great tackle that ended the 1960 championship football game in Philadelphia. Jim Taylor of Green Bay was running forward down the field for a touchdown with a force of 1000 newtons (direction = South). Check Bednardek of Philadelphia runs across the field “at right angles to Taylor’s path” (direction = West) and tackles him with a force of 2500 newtons. Find the resultant of this crash. Find the resultant, which is “resulting” force. What a hit!!!!!

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13. A kite weighs 5 newtons (downward force). A girl throws the kite straight up in the air with a force of 20 newtons. If the wind is blowing horizontally with a force of 20 newtons EAST, find the new force acting upon it. 20 N 5 N 20 N 15 N F

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14. A clock has a minute hand that is 15 in long. Find: - the average speed of the minute hand’s tip. - the inst. speed of the minute hand’s tip as it passes the 3 on the clock. - the displacement of the minute hand’s tip in moving from 1:30 to 1:45. The minute hand’s speed is constant!!! Thus, the instantaneous speed equals.026 m/s 15 dd 45 o 45 – 45 – 90 Triangle

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