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(1) Amelia Earhart learned to fly in a Curtiss JN-4 plane, affectionately known as the Jenny. The Jenny has propellers with 86-inch diameter blades and the center is 7 feet above the ground. The blade in question begins at the three o'clock position and turns counterclockwise. (a) Construct a function of the angle whose output is the horizontal distance of the tip of the propeller blade from the vertical diameter of the propeller. (b) If the propeller makes 1000 revolutions each minute, determine the angular speed in both radians per minute and degrees per minute. (c) The angle swept out by the propeller changes as time passes. In other words, the variable is a function of time. Modify the function you created in part (a) of this question to describe the horizontal distance as a function of time t.

(1) Amelia Earhart learned to fly in a Curtiss JN-4 plane, affectionately known as the Jenny. The Jenny has propellers with 86-inch diameter blades and the center is 7 feet above the ground. The blade in question begins at the three o'clock position and turns counterclockwise. (a) Construct a function of the angle whose output is the horizontal distance of the tip of the propeller blade from the vertical diameter of the propeller. (b) If the propeller makes 1000 revolutions each minute, determine the angular speed in both radians per minute and degrees per minute. (c) The angle swept out by the propeller changes as time passes. In other words, the variable is a function of time. Modify the function you created in part (a) of this question to describe the horizontal distance as a function of time t.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(1) Amelia Earhart learned to fly in a Curtiss JN-4 plane, affectionately known as the Jenny. The Jenny has propellers with 86-inch diameter blades and the center is 7 feet above the ground. The blade in question begins at the three o'clock position and turns counterclockwise. (a) Construct a function of the angle whose output is the horizontal distance of the tip of the propeller blade from the vertical diameter of the propeller. (b) If the propeller makes 1000 revolutions each minute, determine the angular speed in both radians per minute and degrees per minute. (c) The angle swept out by the propeller changes as time passes. In other words, the variable is a function of time. Modify the function you created in part (a) of this question to describe the horizontal distance as a function of time t. (d) Using your equation from part (a), identify the angle(s) at which the tip of the blade is 2 feet right of center, with 0 ≤ 0 < 2TT. (e) Using parts (c) and (d), identify the first two time value(s), t, when the tip of the blade is 2 feet right of center.
Transcribed Image Text:(1) Amelia Earhart learned to fly in a Curtiss JN-4 plane, affectionately known as the Jenny. The Jenny has propellers with 86-inch diameter blades and the center is 7 feet above the ground. The blade in question begins at the three o'clock position and turns counterclockwise. (a) Construct a function of the angle whose output is the horizontal distance of the tip of the propeller blade from the vertical diameter of the propeller. (b) If the propeller makes 1000 revolutions each minute, determine the angular speed in both radians per minute and degrees per minute. (c) The angle swept out by the propeller changes as time passes. In other words, the variable is a function of time. Modify the function you created in part (a) of this question to describe the horizontal distance as a function of time t. (d) Using your equation from part (a), identify the angle(s) at which the tip of the blade is 2 feet right of center, with 0 ≤ 0 < 2TT. (e) Using parts (c) and (d), identify the first two time value(s), t, when the tip of the blade is 2 feet right of center.
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