Trevon drives with velocity v₁ = (55î ─ 10ĵ) mph for 1.0 h, then v₂ = (20î ＋ 50ĵ) mph for 2.0 h. What is Trevon's displacement? Write your answer in component form using unit vectors.

Video transcript

Hey everyone. So this problem is working with velocity vectors. Let's see what they're giving us and what they're asking from us. So we have a particle moving in the wind at a given velocity that lasts for 45 minutes. The wind then changes direction. And the new velocity is also given to us in vector component form and lasts for 1.5 hours were asked to calculate the displacement of the particle giving the results in the component form. So the first thing we can do is recall that velocity is equal to the displacement over time, we can rewrite that as D displacement is equal to V T. And so our total displacement is going to be the sum of our first displacement plus our second displacement. So V one Is given in vector form as 17 I -6 J MPH. And T1 is given as 45 minutes because we're working in units of an hour. I'm going to rewrite that as . powers. And so D one is going to be V one T one, we can rewrite that as 17 I minus six J mph times 0.75 hours. And when we multiply through, we get D1 equals 12.75, I -4. J miles. So we're gonna do the same thing for V two, V 2 Is going to be from the problem five I plus 18J And D and sorry, T two is going to be 1.5 hours. So we're gonna do the same thing to find D two five, I plus 18 J Times 1.5 hours And multiply that through and come up with 7. I plus 27 J mi. So our total displacement Is going to be D one plus D two. And that is going to look like we're going to add the I components and the J components together. So that will look like 12.75, I plus 7. I plus -4.5 J Plus J. And we're still working in units of miles there. And so R D total, It's going to be 20.25, I Plus 22. J. And we can round that to 20.3, I plus 22.5 J around to one digit after the decimal point. And so if we look at our potential answers that aligns with the choice of B 20.3 I plus 22. J mi. So that is the correct answer for this problem. That's all we have for this one. We'll see you in the next video.