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### Course: Precalculus>Unit 6

Lesson 9: Vectors word problems

# Vector word problem: resultant velocity

When an object, say, a boat, travels at a certain velocity, and the medium through which it travels, say, a river, has its own velocity, we can find the resultant velocity of the object by adding the two velocities. In this example, we find the resultant velocity vector of a boat. Created by Sal Khan.

## Want to join the conversation?

• How do we know that we're supposed to add the vectors?
• In 1 dimension, say walking along a moving train, you'd add the train's velocity to yours (one or both of them may be a 'negative' velocity) to work out your velocity relative to the railway track (we're ignoring Einstein's Special Theory of Relativity here, but the error in doing so is truly negligible in almost all everyday scenarios).
So adding velocity vectors in 2 dimensions is entirely consistent with that.
• stupid question but the effect of the current depends what the boat is floating in right?
what if it was sailing in mercury flowing at 15kmph?
• We assume that the liquid it floats in doesn't provide drag. Realistically, any fluid (water too) offers some resistance to motion, which isn't considered here. So, irrespective of the fluid, the motion remains the same assuming the current's velocity is the same.
• this is so helpful can we find more video like this 1
• go to vector unit in precalc
• Why can't you just do the square root of 26^2 + 15^2 to work out the boat's speed?
(1 vote)
• You can only do the Pythagorean theorem if it's a right triangle.

In this case, since the 26-magnitude vector is at 300° CCW from the east and the 52-magnitude one is at 25°, there is a 95° angle between them when you make the triangle for adding the two vectors (). This is not a right triangle, so you can't use Pythagorean.

If you found the angle between the two vectors to be 90°, then you can use Pythagorean to find the magnitude of their sum. (But tbh, it's simpler to add the vectors normally than check the angle between the two vectors every time you do a problem like this.)

Hope this helped :)