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### Course: Class 11 Physics (India)>Unit 8

Lesson 10: Relative motion in 2D

# Relative velocity in 2D

How fast is the sheep moving as seen by the lion? In previous videos, we have already seen how to calculate relative velocity in 1D. In this video let's extend this concept to the next level, to 2D motion. Created by Mahesh Shenoy.

## Want to join the conversation?

• If the equation is velocity of the sheep minus the velocity of the lion then that would equal 1m/s not 5m/s. Saying that that was the equation completely negated everything he said about the Pythagorean theorem
• i had the same question but i got it cleared now. The reason its 5m/s and not 1m/s is because the velocity of the sheep and the velocity of the lion are vector quantities and we add them using vector operations,so its basically 4i+(-3j) which is equal to whole root of 4^2+3^2
• At I don't understand how the generic one dimensional formula for relative velocity is derived. How is it a matter of subtraction when if we were to subtract it, it clearly wouldn't be? Thanks in advance! :)
• Vector subtraction would simply mean that the negative vector is going to be the original vector in the opposite direction. It would still be addition, with the negative vector pointing the opposite way.
• At why we have taken tartlets why not sin or cos for finding direction
• Sin is relation between perpendicular and hypotenuse
cos is relation between base and hypotenuse
tan is relation between perpendicular and base
we were required to find the relation between perpendicular and base, that's why we used tan relation
(1 vote)
• I have trouble with that formula and the resultant.That is the resultant of the two vectors, that is velocity of the sheep 4m/s and the velocity of the lion 3m/s comes out to be 5m/s. But by formula he mentioned "At , comes out to be 1m/s.How it could be?
(1 vote)

*A brief summary:*
To add vectors (in this case forming a right angle) we use the Pythagorean theorem, NOT simply adding the vector magnitudes. So in this case using the Pythagorean Theorem, we would get

3^2 + 4^2 = x^2, which solving for x would give us 5 m/s as the magnitude of the vector.

To specify the direction, you have to give the angle (in this case makes with the x-axis). We can do this with trigonometric ratios, cleanly explained in the video, and if you have any questions relating trignometry, check out the Khan Academy trignometry playlist here: https://www.khanacademy.org/math/trigonometry

This is how we got the result! :)
If you have any further questions, feel free to reach out, and I'll be happy to answer your questions!! :D