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3.6 Motion Problems

3.6 Motion Problems. Today’s Date: 10/6/11. . Currents. Still water: Downstream: faster still water rate + rate of current Upstream: slower still water rate – rate of current. (with current). (against current). Example 1 (#2 on WS).

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3.6 Motion Problems

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  1. 3.6 Motion Problems Today’s Date: 10/6/11 

  2. Currents Still water: Downstream: faster still water rate + rate of current Upstream: slower still water rate – rate of current (with current) (against current)

  3. Example 1 (#2 on WS) In Prairie Dog Creek, Geri can row 60 km downstream in 4 hours or she can row 36 km upstream in the same amount of time. Find the rate that she rows in still water and the rate of the current. Let x = rate in still water c = rate of current Downstream Rate = x + c Upstream Rate = x – c Rate • Time = Distance Downstream: (x + c) • 4 = 60 Upstream : (x – c) • 4 = 36  4x + 4c = 60  4x – 4c = 36 8x = 96 x = 12

  4. Example 1 cont.. x = 12 Find c: 4x + 4c = 60 4(12) + 4c = 60 48 + 4c = 60 4c = 12 c = 3 Rate of current = 3 mph Rate in still water = 12 mph

  5. Wind With the wind: faster still air rate + rate of wind Against the wind: slower still air rate – rate of wind

  6. Example 2 (#7 on WS) A jet liner flying east with the wind traveled 3600 km in 6 hours. The return trip, flying against the wind, took 8 hours. Find the rate at which the jet flew in still air and the rate of the wind. Let x = rate in still air w = rate of wind With Wind Rate = x + w Against Wind Rate = x – w Rate • Time = Distance With Wind: (x + w) • 6 = 3600 Against Wind : (x – w) • 8 = 3600  6x + 6w = 3600  8x – 8w = 3600 (6x + 6w = 3600)(4) (8x – 8w = 3600)(3) 24x + 24w = 14400 24x – 24w = 10800

  7. Example 2 cont.. 24x + 24w = 14400 24x – 24w = 10800 48x = 25200 x = 525 Now find w: 6x + 6w = 3600 6(525) + 6w = 3600 3150 + 6w = 3600 6w = 450 w = 75 Rate in still air: 525 km/h Rate of wind: 75 km/h

  8. Example 3 (#3 on WS) TOO In Blue River, Terry can row 36 km downstream in 3 hours but it takes him 6 hours to row that same distance upstream. Find the rate he rows in still water and the rate of the current. Let x = rate in still water c = rate of current Downstream Rate = x + c Upstream Rate = x – c  6x + 6c = 72  6x – 6c = 36 Downstream: (x + c) • 3 = 36 Upstream : (x – c) • 6 = 36  3x + 3c = 36  6x – 6c = 36 12x = 108 x = 9 Find c: 3(9) + 3c = 36 3c = 9 c = 3 still water = 9 km/h current = 3 km/h

  9. Homework #9 Motion Problems WS Front and Back!! (back is D and R Review)

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