A jet plane taking off from an aircraft carrier has acceleration ...

Question

A jet plane taking off from an aircraft carrier has acceleration a = ( 15 m/s², 22° above horizontal). What are the horizontal and vertical components of the jet's acceleration?

Accepted Answer

Hi, everyone in this problem, we are asked to calculate the acceleration in the X and Y components of the ski jumper, which will have an acceleration of magnitude eight m per second square just before he leaves the ramp. And we know that from the problem statement, the ram will make an angle of 18 degrees counterclockwise with respect to the horizontal. So first, what we want to do is to draw the diagram of our system that we have with the ski jumper leaving the ram. So in this case, I will have just a, just the ground here with a ramp and I will have a ski jumper right at the edge of it just like so and we know that the Ram will make an angle data of degrees with respect to the horizontal counterclockwise, the ski jumper will have an acceleration just like. So an acceleration of eight m per second square and we will, will be asked the X and Y component of the acceleration. So I'm just gonna make an X and Y axis here with respect to the ski jumper itself. So this is the Y and this is gonna be this is gonna be the X just like. So and we are pretty much going to have also, in this case, the angle theta equals 18 degrees here because we will essentially have the same line with two parallel axis here. One is the ground or the land and the other one is the X axis. So we know that this angle is going to be the same with this angle here at 18 degrees. And as always, we want to actually project our acceleration, which is the one that's being asked. So we will have an X component which is A X and also a Y component, which is A Y just like so Okay. So it is given that the ski jumpers acceleration just before leaving the Ram makes an angle of 18° above the horizontal. So in this case, we want to actually use the econometric ratios to determine the values of the A X and also A Y. So we want to recall that the co sign cosign theta is going to equal adjacent over the hypothalamus. And that will Ashley drawing re drawing this small triangle that we have here that will actually corresponds to this is going to be A Y just putting this projection to this side, there's going to be A X and this is going to be a. So in this case, the adjacent over the hypothalamus is going to be A X over A and we want to recall the sign of data is going to be the opposite over the hypothalamus and that will be A Y over A just like. So, so we want to substitute D A and the data with our values to solve for A X and A Y. So rearranging this A X will become a multiplied by Kassian of data. We know that the A is going to be eight m per second squared and cosine of theta is coastline of 18 degrees. So in this case, A X Is going to actually be 7.6 m/s squared. And the same goes with A Y A Y will then be a multiplied by sine of theta. Well, we will have a of eight m per second squared multiplied by the sign of 18 degrees. And that will come up to an A Y value of 2. m per second squared. And that will be all for this particular example, we have the eight X value of 7.6 m per second squared and A Y value of 2.47 m per second squared. And that will actually correspond to option D right here. So option D is going to be the answer to this breath this problem. So that will be all for our practice problem for this video. If you guys have any sort 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.

A jet plane taking off from an aircraft carrier has acceleration a = ( 15 m/s², 22° above horizontal). What are the horizontal and vertical components of the jet's acceleration?

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