Draw each of the following vectors. Then find its x- and y-components. (a) v = (7.5 m/s, 30 degrees clockwise from the positive y-axis)

Video transcript

Welcome back, everyone. We are tasked with sketching the velocity vector. For the following scenario, we are told that we have a hiker that is moving at a speed of 1.5 m per second, 25 degrees counterclockwise from the negative X axis. So here's our negative X axis, here's our negative Y axis. And here is our 25 degree angle measure and our velo or our vector V which has a magnitude of 1.5 m per second. We are tasked with finding what is going to be the X component, our V X and our V Y components for our given vector here. So let's start out with our X component. We can say that the cosine of our angle 25 is equal to V of X divided by our magnitude over our vector 1.5. Now, I'm going to multiply both sides by 1.5. And you'll see that on the left hand side of the equation, the 1.5 is cancel out plugging the right hand side of our equation to, to our calculator, we get 1.36 m per second. And since V is in the negative X and negative Y directions, this will be negative. Wonderful. So now what about V Y here we have, we can say say the similar thing where V Y divided by 1.5 is equal to the sign of our angle 25. Now we will multiply both sides by 1.51 point five cancels out on the left hand side, plugging this into our calculator. We get 0.63 m per second, but it will be negative since V is once again in the negative X in negative wide direction. Let me go ahead and grab all of our work here and I will bring it on down so that we can look at all of our answer choices here and it looks like the answer choice that exactly resembles our findings is going to be answer choice. D Thank you all so much for watching. Hope this, you helped. We will see you all in the next one.