How do I do this trigonometry question?
In the sport of air racing, small planes have to travel between two large towers (or pylons). The gap between a pair of pylons is smaller than the wing-span of the plane, so the plane has to go
through on an angle with one wing ‘above’ the other. The wing-span of a competition airplane is 8 metres.
a. Determine the angle, correct to 1 decimal place, that the plane has to tilt if the gap between pylons is 7 metres
b. Because the plane has rolled away from the horizontal as it travels between the pylons it loses speed. If the plane’s speed is below 96 km/h it will stall and possibly crash. For each degree of ‘tilt’ the speed of the plane is reduced by 0.98 km/h. What is the minimum speed the plane must go through each of the pylons in part a? Write your answer correct to 2 decimal places.
- Anonymous1 year ago
That airplane race is just too dangerous!
- Mike GLv 71 year ago
a) A = 'Tilt'' Angle
cos A = 7/8
A = 28.955°
b) Vmin = Minimum Safe Pylon Speed
Vmin - 0.98A = 96
Vmin = 96+0.98*28.955 = 124.3759
Answer 124.38 km/h
- az_lenderLv 71 year ago
(a) Hypotenuse = 8 meters, Horizontal leg = 7 meters;
the angle is arccos(7/8) = 28.955 degrees, round to 29.0 deg.
(b) This question is poorly phrased. The plane must go through the pylons at 96 km/h. But I think what they want is the speed the plane must have just BEFORE it rolls through the 29-degree angle, in order to maintain 96 km/h when it has tilted.
96 km/h + (0.98 km/h)*29 = 124.42 km/h.
- 1 year ago
I'm so glad I went to community college. The hardest thing I ever had to deal with was navigating the VIA bus system ...and maybe walking home when I missed the bus.