Calculating Height of Prop Tip at 12 Minutes: 2 of 2-Trig

  • Thread starter TonyC
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In summary, the conversation involves calculating the height of a prop tip at a given time based on the speed and radius of the prop blade. The calculations involve radians and degrees and the final answer is 4.14 feet.
  • #1
TonyC
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2 of 2--Trig

Kahleela starts the engine on her small airplane. The engine drives a prop with a radius of 8.5 feet and its centerline 11.5 feet above the ground. At idel, the prop rotates at a constant speed of @ 800 revs/minute. The height of one prop tip as a function of time is given by:
h=11.5+8.5sin(800t), where h is the height in feet and t is the time in minutes. When t= 12 minutes, what is h?

I came up with 7.3 feet...I was wrong...

Where did I stray? :yuck:
 
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  • #2
Radians and degrees? What is the answer?
 
Last edited:
  • #3
a. 4.1 ft
b. 18.9 ft
c. 7.3 ft
d. 15.7 ft
 
  • #4
12*800= 9600. Assuming that is in degrees, which seems most likely, sin(9600)= -0.8660. 8.5sin(9600)= -7.36 (is that where you got the "7.3"? Did you forget the last part?) 11.5+ 8.5sin(9600)= 4.14. The tip of the propellor is 4.14 feet off the ground.
 

1) How is the height of the prop tip calculated at 12 minutes?

The height of the prop tip at 12 minutes is calculated using trigonometry, specifically the tangent function. The formula used is h = d * tan(theta), where h is the height of the prop tip, d is the distance from the observer to the propeller, and theta is the angle of elevation from the observer's line of sight to the prop tip.

2) What is the purpose of calculating the height of the prop tip at 12 minutes?

The purpose of calculating the height of the prop tip at 12 minutes is to determine the vertical position of the propeller in relation to the observer. This information can be used for various purposes, such as monitoring the performance of the propeller or ensuring safe clearance from obstacles.

3) Is the calculated height of the prop tip at 12 minutes accurate?

The calculated height of the prop tip at 12 minutes is an approximation and may not be completely accurate due to factors such as environmental conditions and human error. However, it can provide a close estimate of the actual height of the prop tip.

4) Can the height of the prop tip at 12 minutes be calculated using other methods?

Yes, the height of the prop tip at 12 minutes can also be calculated using other methods such as using a protractor and ruler to measure the angle of elevation and using the Pythagorean theorem to calculate the height. However, trigonometry is often the most efficient and accurate method.

5) What are some potential sources of error when calculating the height of the prop tip at 12 minutes?

Some potential sources of error when calculating the height of the prop tip at 12 minutes include imprecise measurements of the angle of elevation or distance, variations in environmental conditions that may affect the angle or distance, and human error in performing the calculations.

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