In this question. We have this situation, um, toe both living from points p at the same time and travel in the direction shown. So are we need to find the velocity off both a relative to both be and then the time You also need to find the time taken. 4 a.m. b two b uh, 1005 100 ft apart. Okay, so, um, this is a relative velocity problem. Hey, sort off to find the answer. To find a relative velocity. First, we need to write down on the velocity factors the velocity of boats A and B in rectal form. Okay, So based on the given that Graham, uh, we A is 40 kinds. I could sign 60 degrees. I had plus sign 60 degrees jihad. And so this is, uh, 20. I had passed through ST Jihad. Pete second. Okay, then, BB, is it for two. 30 co sign 45 degrees. I had thus sign 45 degrees jihad. And so this is 15 to I had supplies. Jihad sheet second. So the velocity off a relative to be, by definition, is velocity off a minus velocity of B. So putting the numbers together So you have 20 minus 15 to I had class 20 routes three minus 15 to J had. And using your calculator, you get minus 1.21 ahead because 13.4 jihad, Eat four seconds. Okay. So to find a magnitude, you need to find the magnitude. So you take the X component, you square the x component, and you add with square of the white component. Then you take the square it off the some, and you get 13.5 ft per second. And then the direction is attention. The wind component divide by the ex components. You calculate this gets in 4.8 Greece. So this is how the direction looks like. Okay, so this is a velocity off a relative to be, and then this angle is, uh, 84.8 degrees. Okay, then the next thing is to find the time taken. So I'm going to let the time taken for a and B to be 1500 ft putt our wiki. Okay, so, um, we can use the money to a relative velocity. Times time be equal. Set it equal to, uh, 1500. Uh huh. So, um, okay, t would just be 1500. Divide by 13.5. The concrete is you get 111 seconds. All one point. It's five minutes. Okay, so just boxing the answers. So this is the relative, the main two of the relative velocity. Uh, right. The velocity of area to to be. And this is the direction. And then this is the time taken for them to be 1500 ft putt. Okay, And that's all.