qz3sol_3885f10 - river with respect to the ground and the...

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TA: Tomoyuki Nakayama Monday, September 20, 2010 PHY 2048: Physic 1, Discussion Section 3885 Quiz 3 (Homework Set #4) Name: UFID: Formula sheets are not allowed. Calculators are allowed. Do not store equations in your calculator. You need to show all of your work for full credit. ________________________________________________________________________________ A 150-m-wide river flows due west at a uniform speed of 4.00 m/s. A boat with a speed of 12.0 m/s relative to the water leaves the south bank pointed in a direction 15.0º east of north. a) What are the magnitude and direction of the boat’s velocity relative to the ground? We take our +x axis to the east and +y axis to the north. In unit-vector notation, the velocity of the
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Unformatted text preview: river with respect to the ground and the velocity of the boat with respect to water are, respectively, v WG = -4 i , v BW = 12cos75º i + 12sin75º j = 3.11 i + 11.6 j The velocity of the boat with respect to the ground is v BG = v BW – v WG = -0.89 i + 11.6 j The magnitude and direction of vBG are v BG = √ ((-.89) 2 +11.6 2 ) = 11.6 m/s, θ = tan-1 (11.6/(-0.89)) = -85.6 + 180 = 94.4º 4.4 west of north Note that has a negative x component and positive y component. It is in the 2 nd quadrant. b) How long does the boat take to cross the river? To cross the river, the boat must move 150 m in the y direction. Therefore, t = Δ y/v y = 12.9 s...
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