Jack and Jill ran up the hill at 3.0 m/s. The horizontal component of Jill's velocity vector was 2.5 m/s. b. What was the vertical component of Jill's velocity?

Video transcript

Hi everyone in this problem, we will have a box which is tracked on a ramp with a force of eight Newton peril to the surface, so peril to the ramp. And in this case, we will have a ram with an angle of data above the horizontal. And we'll have a horizontal component of the force factor which is six Newton. And we're being asked the vertical component of the force factor itself. So I'm gonna first start us off with creating an illustration diagram of our system. So in this case, for example, we will have a ram here with an angle theta and a box here which will have a force parallel to Durham itself here At eight Newton just like. So, and as always, we will have the projection of each force in the X and the Y direction. So I'm going to make an X and A Y access to make it easier for us just like. So does this X this is going to be the Y and we will have an Y F Y component here of the projection or a vertical component, which is the one that's being asked and we will have an F X component here which is a horizontal component which is known to be six Newton just like so okay. So now we know that the force factor F, the forest factor half will have a horizontal component F X or in the factor notation in the eye. And we will, it will also have a vertical component in the J direction or in the J. So F really close to F X I plus F Y E J. The components of the force factor F X F Y and F can also be arranged to form a right triangle as shown here where we can actually move this F Y into this side which will create a right angle triangle of the hypothesis being F and then this side being fy this side being F X with the data. The same with this data of the realm here. The Pythagoras theorem states that the square of the hypotenuse us in a right angle triangle which we have here and here in our system is equal to the sum of the squares of the other two sides. So because of that, we know that F squared well equals to F X squared plus F Y squared based on the Pythagoras Terim. So we are being asked what F Y is so rearranging this, we can actually get that F Y will then equal to the square root of F squared minus F X squared. We know what F S we know what F X s so we can solve for F Y, which will essentially just be the square root of eight squared minus six squared. Or I am going to actually include all the units here for completeness. So eight Newton squared minus six Newton squared And that will be our FY which will correspond to 5.3 Newton. So 5.2 Newton of FY component will actually be the answer to this practice problem which will correspond to option b. So option B will be the answer and that will correspond to the particular component of the force f. And that will be all for this particular practice problem. If you guys have hundreds of confusion, please make sure to check out our other lesson videos on similar topics and that will be all for this video. Thank you.