Susan, driving north at 60 mph, and Trent, driving east at 45 mph, are approaching an intersection. What is Trent's speed relative to Susan's reference frame?

Video transcript

Hey, everyone. Today we're dealing with the problem regarding relative velocity. So today we're being told that to circus artists ride two unicycles, the artist dressed in red has a velocity of V R is 1.5 m per second and the one dressed in blue has a velocity of VB two point negative 2.5 m per second. With this information, we're being asked how fast the artist dressed in blue appears to be moving compared to the artist dressed in red, appears to be moving. So let's think about this and let's write down what we have so far. The velocity the red artist is given with respect to a fixed frame on earth, right? So let's say that the velocity of the red artist is given with the regards to a fixed or with respect to a fixed fixed frame on earth. That's hard to say And that is 1. I meters per second. Similarly, the blue artist has also been given with respect to earth blue over e With respect to earth and that is negative 2.5 J m/s. So we'll calculate the first we'll calculate first, the velocity of the blue artist with respect to the red one. Now, the velocity of the blue artists relative to the red is equal to its velocity relative to the earth frame plus the velocity of the earth frame relative to the artist. What does that mean? Well, the and let's write this here in blue, the velocity of blue with respect to read will therefore be equal to the velocity of the blue with respect to the earth plus the velocity of the earth with respect to the red artist, which we can also write as velocity of blue with regards to E minus the velocity of are with respect to E where E is the fixed frame on earth. So rewriting that we get -2.5 J m/s minus 1.5 I meters per second. Let me just put those in the practices. So that gives us our velocity. But we're not, well, that gives us our velocity with respect to earth or with respect to the oh of blue with respect to our, but we need to find how fast the artist appears to the red artist. So we need to actually find the magnitude or calculate the speed of V V over R. And to do this to calculate magnitude B over R, we take the square root of the sum of squares, square root of the summer squares. So that'll be -1.5, meters per second, all squared plus negative 2.5 m per second squared Will give us an answer of 2.9 m/s. So The artisan blue appears to be moving at a speed of 2.9 m/s with respect to the artist dressed in rent. I hope this helps and I look forward to seeing you all in the next one.