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phy131studiof16:lectures:chapter3b [2016/09/12 08:53] mdawber [Relative Velocity with Vector Sums] |
phy131studiof16:lectures:chapter3b [2016/09/12 09:22] (current) mdawber [Crossing a river] |
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We need to draw the diagram using the known angles to set up the problem to find the speed the swimmer should maintain. | We need to draw the diagram using the known angles to set up the problem to find the speed the swimmer should maintain. | ||

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+ | ===== Problem 3.70 - the problem I meant to assign instead of 3.7 ===== | ||

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+ | Relative to the water, the boat has a known velocity $v_{BW}$ (including direction $\theta_{BW}$). | ||

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+ | The direction of the boat's velocity relative to the land can be deduced as $\tan\theta_{BL}=\frac{120\mathrm{m}}{280\mathrm{m}}$. | ||

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+ | {{3_70_1.png}} | ||

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+ | ===== Problem 3.70 solution ===== | ||

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+ | |{{3_70_2_sine.png}}| Use the sine rule. \\ $\frac{v_{WL}}{sin(\theta_{BW}-\theta_{BL})}=\frac{v_{BW}}{sin(90^{o}+\theta_{BL})}=\frac{v_{BL}}{\sin(90^{o}-\theta_{BW})}$ | | ||

+ | |{{3_70_2_components.png}}| or use components. \\ $\frac{v_{BW}\sin\theta_{BW}-v_{WL}}{v_{BW}\cos\theta_{BW}}=\tan\theta_{BL}$. | | ||

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+ | (Recall that $\tan\theta_{BL}=\frac{120\mathrm{m}}{280\mathrm{m}}$). |