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nguyen777
i have a physics question an airplane is flying horizontally at a velocity of 50 m/s at an altitude of 125m. It drops a package to observes on the grown below. Approximately how far will the package travel in horizontal direction from the point it was dropped?
Draw its vector components. So on the x-axis you have a velocity ( without accounting for anything like air resistance, etc...) and you have acceleration on the y axis, you can use pythagorean theorem afterwards when you solved for your vectors^^
but it gave me velocity though and the altitude how will i find the other sides
velocity on the x-axis so it will look like this ( sorry for the bad drawing) |dw:1367376838569:dw|
|dw:1367376962352:dw|
so you can find the time it takes to get on at the ground ( vertically) and then solve for your velocity. Afterwards use pythagorean theorm to find the speed of the resultant vector and because you have the total time it took to reach the ground you just plug it in and solve for your x of the resultant vector
so that is what i have so would i be looking for the hypotenuse?
Yes you would but in order to do so you ahve to find the VELOCITY vector for the y. Because you only have the acceleration and height you can find the amount of time it took to reach ( and you have the initial time = 0 second) so solve for T final using your kinematics equation. Once you have T final you can solve for the average velocity ( Distance travelled / delta in time ) afterwards solve for the hypothenuse
or, simply plugging it into the equations, since the package was initially moving with a horizontal velocity of 50 (same with the plane), \(\vec S_f=\vec S_i + \vec u t + \frac{1}{2}\vec a t^2\) now, \(\vec u=50\hat i\), \(\vec a=-10\hat j\),\(\vec S_f=S_{fx}\hat i+0 \hat j\) and \(\vec S_i=125\hat j\), taking the ground as my x-axis, \(S_{fx}\hat i+0 \hat j=125\hat j +50\hat i t - \frac{1}{2}10\hat j t^2\) equating equal vectors, \(0=125\hat j - \frac{1}{2}10\hat j t^2\)....(1) \(S_{fx}\hat i=50\hat i t \)....(2) from(1), t=5. subbing that into (2) gives \(S_{fx}=250m\) do you need further help?