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qz3sol_3891f10 - river with respect to the ground and the...

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TA: Tomoyuki Nakayama Tuesday, September 21, 2010 PHY 2048: Physic 1, Discussion Section 3891 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 180-m-wide river flows due east at a uniform speed of 3.00 m/s. A boat with a speed of 8.00 m/s relative to the water leaves the north bank pointed in a direction 15.0º west of south. 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 = 3 i , v BW = 8cos(-105º) i + 8sin(-105º) j = -2.07 i – 7.72 j The velocity of the boat with respect to the ground is v BG = v BW + v WG = 0.93 i – 7.72 j The magnitude and direction of v BG are v BG = √ (.93 2 +(-7.72) 2 ) = 7.78 m/s, θ = tan-1 ((-.7.72)/.93) = -83.1º, 6.9º east of south. Note that v BG has a positive x component and negative y component. It is in the 4 th quadrant. b) How long does the boat take to cross the river? To cross the river, the boat must move 180 m in the negative y direction. Therefore, t = Δ y/v y = 23.3 s...
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