Problema Solution
The track of the Duquesne Incline in Pittsburgh, Pennsylvania is about 800 feet long at an angle of elevation of 30 degrees. The average speed of the cable cars is about 320 feet per minute. How high does the Duquesne Incline rise? What is the vertical speed of the cable cars (in feet per minute)?
Answer provided by our tutors
Let's call the length of the track "c" and the height "a".
You know that the sine of an angle is the opposite over the hypotenuse (in a right triangle).
In this case, sin(30) = height/length = a/c
Therefore a = c*sin(3)
So the height is 800*sin(30) = 400 ft (because sin(30) = 0.5)
Speed is a vector, so it has a vertical and a horizontal component. Let's call the vertical speed "A".
Again using the sin formula, you have A/320 = sin(30) so A = 320*sin(30) = 160 ft/min.
So the answers are:
height = 400 feet
vertical speed = 160 feet per minute