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101e104 - Physics 171.101 Exam 1 Feb 19 2004 Prof Barnett...

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Unformatted text preview: Physics 171.101 Exam 1 Feb. 19, 2004 Prof. Barnett Do all problems. Everything should be written in ink. You are allowed to use material written on one 3"x‘o 1. [Q ")7 index card. _, A Consider the vectors [T : —3i + 3j + 9k and B 2 2i — 43 + 2 e. .. ,1 A) (10 pts) Find a unit vector which is parallel to A B) (10 pts) Find the angle between .4 and B. The Parliament Building in London, England has a large Clock, often called “Big Ben”. Deﬁne the X direction as pointing from the center of the clock to the “3” and the Y direction as pointing from the center of the clock to the “12”. At 12:00 noon its hour and minute hands point “up”. Big Ben’s minute hand is 2.5 meters long. A) (7 pts) What is the angular velocity, Q, of the tip of its minute hand at noon? B) (6 pts) What is the linear velocity, 17, of the tip of Big Ben’s minute hand at noon? C) (7 pts) What is the acceleration, d, of the tip of Big Ben’s minute hand at noon? ) ., WEI/56¢. A rabbit is eating carrots in a farmer’s garden when it sees the farmer’s dog running towards it. The rabbit runs in a straight line to its burrow taking 3 seconds to get there. The velocity of the t, rabbit versus time is shown in the adjacent diagram_ . ,V .er. ._ 2? {3% sister: A) (10 pts) Find the acceleration of the rabbit at all times during its dash. Drawa graph showing the acceleration versus time. B) (10 pts) How far did the rabbit go during its 3 second dash? « The rabbit in the previous problem waits For the dog to go home and then sticks it head up out of its burrow intending to go back to the garden for some more carrots. A hawk swoops down and grabs it and flies away with it at a constant velocity of 177mm m (m, — 2.0“; ' 1.5} I 10/}. ”L, where X and Y are horizontal directions and Z is I SEC ﬂ. vertical. The wind has a velocity relative to the ground of VW to Wound : 1.0i—0.5j sec. Four seconds after the hawk grabs the rabbit the farmer sees the hawk and ﬁres a shotgun at it, but rnisses both it and the rabbit. The hawk is frightened by the blast and drops the rabbit which lands unhurt on the ground. Use l g l: 10 3:22. A) (8 pts) “that is the “hawk & rabbit” velocity relative to the ground when the farmer shoots at them? B) (8 pts) \Vhat is the location of the hawk and rabbit relative to the rabbit’s burrow when the farmer shoots at them"? C) (8 pts How much time passes from when the hawk grabs the rabbit until the rabbit lands safely on the ground? D.) (S ptsl Where is the rabbit. relative to its burrow when it lands on the ground? ‘ / >ts'; \Vhat is the rabl'iits velocity just belore it lands on the ground.7 ...
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