Height question

Apr 2010
40
0
The maximum angle of a climb for a certain light aircraft is 9 degrees. A line of electric wires 20m above the ground is located 120m from the end of the runway. Will the aircraft clear the wires after takeoff?

If you don't know which ones higher, how do you draw the diagram?
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
Draw right triangle with the base 120m and the height 20m. The angle on the base opposite of the 90 degree angle is 9 degrees
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
The base shouldn't be broken up. The whole bottom is 120 not 120+x
 
Apr 2010
40
0
Then wheres the 9 degrees is it on the most left angle?
 
Apr 2010
40
0
I got x=60. I got my h value as approximately 9.5m. The book says you need to have a climb angle of 9.5 degrees to clear the wires but I did the calculation and I only get 10 degrees.
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
You need to solve for min angle:

\(\displaystyle tan(\theta)=\frac{y}{x}\)

x and y correspond to the x and y axis not the 60 you obtained. Make sure your calculator is in degrees not radians.
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
Then is h 9.5m?
\(\displaystyle \theta=arctan\bigg(\frac{20}{120}\bigg)=9.46\)

So in order to clear the wire, the plane needs to leave at an angle of 9.46 degrees from 120m away.
 
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