So we see how Parametric equations are extremely helpful in determining, um, these types of real life application problems. Why, since we take this originally equation right here, um, plugging in 51.2 we get the y equals 12 755 m and then for X, we get plugging in, um, 102.4 So double the 51.2 we end up getting the X equals 88,366 0.4 m. Um, and then using this trajectory in part B, we see that plugging in, um 51.2 We will determine that. 90 squared? Um, and obviously you could use, um, a graphing calculator to get the best representation.īut a decent look at the trajectory would be something like this. If we plug in our values to the original equation actually equal 500 Route three t and then why is going to equal 500 T minus 4. Since Alfa is 30 degrees, we'll see that X will end up equaling. Pressing the respective shortcut again will get you back to normal text. For subscript, press CTRL + (press and hold Ctrl, then press ). For superscript, simply press Ctrl + Shift + + (press and hold Ctrl and Shift, then press +). Then using a graphing utility to sketch the trajectory. You can do this through the Font dialog box, but there is a much faster way. We're in this case a is tangent of Alfa and B is this whole thing right here? So based on that, we see that it lies the trajectory projectile lies on the graph of the quadratic polynomial y equals a X plus B x squared. If our input was pi, then we input into our function and then f of pi - when x is pi, were going to output f of pi, which is equal to 2 over pi. Then, um, this is essentially equal to a X plus B x squared. So were able, for that input, were able to find an output. But instead of T v X over v, not Costa Alfa squared then, um, we can combine some things and we see that sign over cosign we know is tangent and then the V knots will cancel so we'll actually be left with tangent of Alfa Times X plus a negative g over, uh to from the one half v not squared Crow sine squared off Have two x squared. And then we'll want to plug this into the white equation so we'll get y equals the not sign of Alfa Times X over v not cosign Alfa minus one half g t squared. Finding our t value and what we see is that when we saw for it, we'll get that t is equal to X over the not co sign uh Alfa.Īnd that's by dividing this whole thing by v not cosign Alfa and solving for team. And then we are subtracting the one half g t squared where G is gravity, so 9.8 m per second squared. So we're given that X equals V not initial velocity co sign of Alfa Times T and why similarly equals V not, but it's times the sign of Alfa, uh, times teeth. Calcpad Calcpad Version 5.6 quick reference guide 34-36 Peyo Yavorov blvd, Sofia 1164, Bulgaria +359 How it works 1. $\begin ]$ are designed to be worked with the aid of a "Matrix program" (a computer program, such as MATLAB, Maple, Mathematica, Math Cad, or Derive, or a programmable calculator with matrix capabilities, such as those manufactured by Texas Instruments or Hewlett-Packard). In a wind tunnel experiment, the force on a projectile due to air resistance was measured at different velocities:
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