cintinative Posted July 1, 2022 Share Posted July 1, 2022 An ocean current flows due south at 10 km/h. If a ship is going to travel through this current on a course with bearing 120 degrees at a speed of 20 km/h, find its heading. We are not coming up with the appropriate heading, and I suspect we are drawing it incorrectly. There is no solution key for this problem, unfortunately. Just an answer. Quote Link to comment Share on other sites More sharing options...
EKS Posted July 1, 2022 Share Posted July 1, 2022 What does the answer key say is the answer? Quote Link to comment Share on other sites More sharing options...
cintinative Posted July 1, 2022 Author Share Posted July 1, 2022 3 minutes ago, EKS said: What does the answer key say is the answer? 90 degrees Quote Link to comment Share on other sites More sharing options...
EKS Posted July 1, 2022 Share Posted July 1, 2022 What did you get? Quote Link to comment Share on other sites More sharing options...
cintinative Posted July 1, 2022 Author Share Posted July 1, 2022 3 minutes ago, EKS said: What did you get? 139.1 degrees =( Quote Link to comment Share on other sites More sharing options...
EKS Posted July 1, 2022 Share Posted July 1, 2022 9 minutes ago, cintinative said: 139.1 degrees =( That's what I got too. 1 Quote Link to comment Share on other sites More sharing options...
cintinative Posted July 1, 2022 Author Share Posted July 1, 2022 21 minutes ago, EKS said: That's what I got too. interesting. So maybe the answer key is wrong? Quote Link to comment Share on other sites More sharing options...
regentrude Posted July 1, 2022 Share Posted July 1, 2022 (edited) @cintinativeand @EKS: I AM getting 90 degrees. Can the problem be that you switched bearing vs heading? Bearing is the final resultant velocity, and heading is the direction in which the ship is pointing. Velocity addition in vectors: V_ocean+V_ship=V final In x-y components, with x = east and y= North: V0x+Vsx=Vfx and voy+Vsy=Vfy Let's look at y first: Voy=-10 (i.e. 10 km/h due South) Vfy= - 20 sin 30 degrees (bearing of 120 means 120 CW from N, so 30 below x-axis; y is opposite side, hence sine) Vfy= -20* 1/2 = -10 Thus VSy=0, no S/N velocity component of the ship - ship must move due East, i.e. at 90 degrees. Did I mess up? Edited July 1, 2022 by regentrude 1 1 Quote Link to comment Share on other sites More sharing options...
cintinative Posted July 1, 2022 Author Share Posted July 1, 2022 (edited) Here is our drawing. I think that the big difference is that regenetrude drew the current first and then the direction of the boat off of the same point. This is why I wanted to have someone draw a picture. I think ours is drawn incorrectly. Sorry for the bad picture. Edited July 1, 2022 by cintinative Quote Link to comment Share on other sites More sharing options...
regentrude Posted July 1, 2022 Share Posted July 1, 2022 (edited) 2 minutes ago, cintinative said: We were wondering if perhaps the river current works like wind direction where it comes from behind? Here is our drawing. I really think our problem is how it is drawn perhaps? Or where we are reading the degree measurement? Sorry for the bad picture. Your pic looks like you have ADDED the ocean velocity to the final (i.e. bearing) velocity given in the problem. The final velocity is the SUM of the ocean current and the ship's heading velocity. In other words: if the ocean current already gives the ship all its needed South component of velocity, the ship does not need any heading velocity to the south; it can head straight East and will end up with the 120 degree bearing. Edited July 1, 2022 by regentrude 1 Quote Link to comment Share on other sites More sharing options...
EKS Posted July 1, 2022 Share Posted July 1, 2022 I was hoping regentrude would chime in! 1 Quote Link to comment Share on other sites More sharing options...
Malam Posted July 1, 2022 Share Posted July 1, 2022 Where is this problem from? Quote Link to comment Share on other sites More sharing options...
cintinative Posted July 1, 2022 Author Share Posted July 1, 2022 3 hours ago, Malam said: Where is this problem from? Dolciani Algebra 2 with Trigonometry Quote Link to comment Share on other sites More sharing options...
Malam Posted July 1, 2022 Share Posted July 1, 2022 30 minutes ago, cintinative said: Dolciani Algebra 2 with Trigonometry Does it teach vectors? Quote Link to comment Share on other sites More sharing options...
cintinative Posted July 2, 2022 Author Share Posted July 2, 2022 (edited) 2 hours ago, Malam said: Does it teach vectors? yes, this is a copy of part of the TOC. My edition is older than this one though. Edited July 2, 2022 by cintinative Quote Link to comment Share on other sites More sharing options...
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