-8.0 × 10-3 m ' A student club is designing a trebuchet for launching a pumpkin into projectile motion. Based on an analysis of their design, they predict that the trajectory of the launched pumpkin will be parabolic and described by the equation y(x) = ax² + bx where a = − b = 1.0 (unitless), x is the horizontal position along the pumpkin trajectory and y is the vertical position along the trajectory. The students decide to continue their analysis to predict at what position the pumpkin will reach its maximum height and the value of the maximum height. What is the derivative of the vertical position of the pumpkin trajectory with respect to its horizontal position? ▸ View Available Hint(s) О dy 33 33 33 = 2ax + b dx dy = 0 dx dy 2ах dx dy ax dx Submit Part B Previous Answers Correct In order to evaluate the maximum of a function a first step is to obtain the derivative of the function. In order to find the value of the horizontal position of the pumpkin for which its height is a maximum, we need to seek values of xm for which: ▸ View Available Hint(s) dy dx -= 2axm + b = Ymax, which will be determined in the next step of the analysis dy = 2axm+b=0 dx 2 ○ y(x) = axm² + b = 0 d²y dy 2axmb has its minimum value, which must be determined by obtaining dx2 dx
-8.0 × 10-3 m ' A student club is designing a trebuchet for launching a pumpkin into projectile motion. Based on an analysis of their design, they predict that the trajectory of the launched pumpkin will be parabolic and described by the equation y(x) = ax² + bx where a = − b = 1.0 (unitless), x is the horizontal position along the pumpkin trajectory and y is the vertical position along the trajectory. The students decide to continue their analysis to predict at what position the pumpkin will reach its maximum height and the value of the maximum height. What is the derivative of the vertical position of the pumpkin trajectory with respect to its horizontal position? ▸ View Available Hint(s) О dy 33 33 33 = 2ax + b dx dy = 0 dx dy 2ах dx dy ax dx Submit Part B Previous Answers Correct In order to evaluate the maximum of a function a first step is to obtain the derivative of the function. In order to find the value of the horizontal position of the pumpkin for which its height is a maximum, we need to seek values of xm for which: ▸ View Available Hint(s) dy dx -= 2axm + b = Ymax, which will be determined in the next step of the analysis dy = 2axm+b=0 dx 2 ○ y(x) = axm² + b = 0 d²y dy 2axmb has its minimum value, which must be determined by obtaining dx2 dx
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter4: Motion In Two Dimensions
Section: Chapter Questions
Problem 42AP: A pendulum with a cord of length r = 1.00 m swings in a vertical plane (Fig. P4.42). When the...
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Transcribed Image Text:-8.0 × 10-3 m '
A student club is designing a trebuchet for launching a pumpkin into projectile motion. Based on an analysis of their design, they predict that the trajectory of the launched pumpkin will be parabolic and described by the equation y(x) = ax² + bx where a = −
b = 1.0 (unitless), x is the horizontal position along the pumpkin trajectory and y is the vertical position along the trajectory. The students decide to continue their analysis to predict at what position the pumpkin will reach its maximum height and the value of the maximum height.
What is the derivative of the vertical position of the pumpkin trajectory with respect to its horizontal position?
▸ View Available Hint(s)
О
dy
33 33 33
=
2ax + b
dx
dy
= 0
dx
dy
2ах
dx
dy
ax
dx
Submit
Part B
Previous Answers
Correct
In order to evaluate the maximum of a function a first step is to obtain the derivative of the function.
In order to find the value of the horizontal position of the pumpkin for which its height is a maximum, we need to seek values of xm for which:
▸ View Available Hint(s)
dy
dx
-= 2axm + b = Ymax, which will be determined in the next step of the analysis
dy
=
2axm+b=0
dx
2
○ y(x) = axm² + b = 0
d²y
dy
2axmb has its minimum value, which must be determined by obtaining
dx2
dx
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