June 12th, 2019, 01:26 PM  #1 
Member Joined: Feb 2018 From: Iran Posts: 50 Thanks: 3  Relative motion in two dimension In a 300 m wide river, flowing with a velocity of 1 m/s, two boats, one with a velocity of v1 = 20 m/s relative to the Earth and the other with a velocity of v2 = 15 m/s relative to the river, start moving from point K, as shown in the figure. What will the distance between the boats be when they reach the other side of the river? 
June 12th, 2019, 01:45 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,940 Thanks: 1545 
boat #1 ... $v_{x_1} = 20\cos(37) + 1 \approx 17 \text{ m/s}$ $v_{y_1} = 20\sin(37) \approx 12 \text{ m/s}$ boat #2 $v_{x_2} = 15\cos(53)  1 \approx 8 \text{ m/s}$ $v_{y_2} = 15\sin(53) \approx 12 \text{ m/s}$ Use the velocity in the ydirection to calculate the time required to displace 300 m for each boat, then determine their respective displacements in the xdirection from position K to determine $\Delta x_1  \Delta x_2$ 
June 12th, 2019, 10:16 PM  #3  
Member Joined: Feb 2018 From: Iran Posts: 50 Thanks: 3  Quote:
 
June 13th, 2019, 04:20 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,940 Thanks: 1545 
my mistake ... Boat #1’s velocity is w/respect to the earth ... that means its velocity in the xdirection already takes the current into account. $v_{x_1} = 16 \, m/s$ So, relative motion in the x direction is 16  (8 ) = 24 m/s 25 seconds to cross the river results in 600 m separation. 

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