Find the xmax, ymax, and v o x from the parabolic equation given in the graph. P

Question

Find the xmax, ymax, and vox from the parabolic equation given in the graph. Put it in the form of the equation for y(x) as shown below. Please show all work.

The formula for y (x) is

where yMAX and xMAX are the y- and x-coordinates of the projectile at its maximum altitude. By fitting the y versus x data, we can determine the values of yMAX, xMAX, and vox.

Verify that the trajectory (y(x)) is a parabola for the 2D projectile motion data. To do this, go back to your scatter plot (y vs. x) of this data and fit it to a parabolic function of the form in the equation above. You will have to use the non-linear fitting button and then pick the quadratic function and modify it to look like the equation above. Hint: use the value of g (9.8) in S.I. units and let the symbols, A, B, and C represent the variables zMAX, xMAX, and vox. The fitted values of zMAX, xMAX, and vox will be part of your results.

Explanation / Answer

given formula for y(x)
y(x) = ymax - (g/Vox^2*2)[ x - xmax]^2

now the graph equation is given as
y(x) = -2.1741x^2 + 3.1146x - 0.0454

comparing both the equations we see
g/Vox^2*2 = 2.1741x
using g = 9.81 m/s/s
Vox = 1.51148 m/s

similiarly
g*xmax/Vox^2 = 3.1146
9.81*xmax/1.51148^2 = 3.1146
or xmax = 0.72533 m

similiarly
y max - (g/Vox^2*2)xmax^2 = -0.0454
y max - (9.81/1.51148^2*2)*0.72533^2 = -0.0454
ymax = 1.08417 m

hence the equation of the graph can be written as
y(x) = 1.08417 - (g/2*1.51148^2)[ x - 0.72533]^2

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