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 = −8.0 × 10−³ m−¹, 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) dy dx = 2ax + b dy dx dy dx dy dx - 0 = 2ax ax

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
Chapter10: Rotational Motion
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Problem 13OQ: Let us name three perpendicular directions as right, up, and toward you as you might name them when...
Question
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 = −8.0 × 10−³ m−¹,
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)
dy
dx
= 2ax + b
dy
dx
dy
dx
dy
dx
-
0
= 2ax
ax
Transcribed Image Text: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 = −8.0 × 10−³ m−¹, 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) dy dx = 2ax + b dy dx dy dx dy dx - 0 = 2ax ax
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