Now assuming negligible aerodynamic drag, the equations governing the "flight" of the ball are given as: x = xo +Voxt 1 29t² y = yo + Voyt - The first of these equations can be used to isolate t and express it as a function of x (as done in class). Then this expression for t can be substituted into the second equation to obtain an equation for y as a function of x (as done in class). Finally, this equation can be simplified and put into the standard form of: y = ax² + bx + c Perform this process and compare the result to the trendline equation to determine the "launch" speed of the ball Vo.

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter1: Introduction And Vectors
Section: Chapter Questions
Problem 70P
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In each my sections of MCEG 1101 (PO1 & P02), a student was asked to toss a tennis ball in front of the
screen upon which a grid was projected. Based on my slow-motion video recording of the ball tossed in
Section P01, the following data was generated (also see uploaded Excel file "tennis ball toss trajectory").
x (grid units)
1
2
3
4
5
6
verti cal position, y (ft)
4
3.5
2.5
2
Based on these data, a parabolic trendline was developed, as shown in the plot below:
1.5
1
0.5
819
0
7
y (grid units)
0
3
5.3
6.5
6.7
5.8
4
0.9
0.5
1
x(ft)
0.55
1.1
1.65
2.2
2.75
3.3
3.85
4.4
Tennis Ball Toss Data from MCEG 1101-P01
y(ft)
0
1.5
1.65
2.915
3.575
3.685
3.19
2.2
0.495
y = -0.9307x² + 4.7619x - 2.3925
R² = 0.999
2.5
2
3.5
horizontal position, x (ft)
3
4
4.5
5
Transcribed Image Text:In each my sections of MCEG 1101 (PO1 & P02), a student was asked to toss a tennis ball in front of the screen upon which a grid was projected. Based on my slow-motion video recording of the ball tossed in Section P01, the following data was generated (also see uploaded Excel file "tennis ball toss trajectory"). x (grid units) 1 2 3 4 5 6 verti cal position, y (ft) 4 3.5 2.5 2 Based on these data, a parabolic trendline was developed, as shown in the plot below: 1.5 1 0.5 819 0 7 y (grid units) 0 3 5.3 6.5 6.7 5.8 4 0.9 0.5 1 x(ft) 0.55 1.1 1.65 2.2 2.75 3.3 3.85 4.4 Tennis Ball Toss Data from MCEG 1101-P01 y(ft) 0 1.5 1.65 2.915 3.575 3.685 3.19 2.2 0.495 y = -0.9307x² + 4.7619x - 2.3925 R² = 0.999 2.5 2 3.5 horizontal position, x (ft) 3 4 4.5 5
Now assuming negligible aerodynamic drag, the equations governing the "flight" of the ball are given as:
x = xo + Voxt
1
29t²
y = y + Voyt
The first of these equations can be used to isolate t and express it as a function of x (as done in class).
Then this expression for t can be substituted into the second equation to obtain an equation for y as a
function of x (as done in class). Finally, this equation can be simplified and put into the standard form of:
y = ax² + bx + c
Perform this process and compare the result to the trendline equation to determine the “launch" speed
of the ball Vo.
Transcribed Image Text:Now assuming negligible aerodynamic drag, the equations governing the "flight" of the ball are given as: x = xo + Voxt 1 29t² y = y + Voyt The first of these equations can be used to isolate t and express it as a function of x (as done in class). Then this expression for t can be substituted into the second equation to obtain an equation for y as a function of x (as done in class). Finally, this equation can be simplified and put into the standard form of: y = ax² + bx + c Perform this process and compare the result to the trendline equation to determine the “launch" speed of the ball Vo.
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