A pilot flies a plane that averages approximately 210 km/hr. The plane leaves point A at a bearing of 40 degrees and flies two hours to point B. After a brief stop the plane leaves point B at a bearing of 125 degrees and flies for another 30 minutes before landing at point C. If the pilot wishes to fly from point C back to point A, determine:
a) The distance from point C to A
b) The bearing at which the pilot will have to fly to return to point A.
d1 = 210km/h * 2h = 420 km @ 40 Deg.
d2 = 210km/h * 0.5h = 105 km @ 125 Deg.
X=hor.=420*cos40 + 105*cos125 = 262 m.
Y=ver.=420*sin40 + 105*sin125 = 356 m.
tanA = Y/X = 356 / 262 = 1.35878.
A = 53.6 Deg.
a. d = X/cosA = 262 / cos53.6 = 442 m =
Dist. from C to A.
b. Bearing = 53.6 Deg. North of East or
36.4 Deg. East of North.
To solve this problem, we can use trigonometry and vector addition. Here's how we can find the answers:
a) Distance from point C to A:
Step 1: Find the distance from point B to C.
Since the plane flies at an average speed of 210 km/hr for 30 minutes (0.5 hours) from point B to C, the distance traveled can be calculated using the formula: distance = speed × time.
Distance from B to C = 210 km/hr × 0.5 hr = 105 km.
Step 2: Find the distance from point A to B.
Since the plane flies at an average speed of 210 km/hr for 2 hours from point A to B, the distance traveled can be calculated using the formula: distance = speed × time.
Distance from A to B = 210 km/hr × 2 hr = 420 km.
Step 3: Find the total distance from point C to A.
The total distance from C to A can be calculated by adding the distances from B to C and A to B: Distance from C to A = (Distance from B to C) + (Distance from A to B).
Distance from C to A = 105 km + 420 km = 525 km.
Therefore, the distance from point C to A is 525 km.
b) Bearing at which the pilot will have to fly to return to point A:
To find the bearing at which the pilot will have to fly to return to point A, we can use vector addition and trigonometry.
Step 1: Determine the difference in the bearings.
The change in the bearing from point B to C is given as 125 degrees.
Step 2: Find the initial bearing at point A.
Since the bearing at point A is given as 40 degrees, we need to subtract the change in bearing from the initial bearing at point A to find the bearing at point C.
Bearing at point C = Initial bearing at point A - Change in bearing from point B to C
Bearing at point C = 40 degrees - 125 degrees
Step 3: Adjust the bearing.
Since bearings are typically given in the range of 0 to 360 degrees, we need to adjust the bearing at point C to fall within this range.
If the bearing at point C is negative, we can add 360 degrees to make it positive.
Bearing at point C = 40 degrees - 125 degrees + 360 degrees
Bearing at point C = 275 degrees.
Therefore, the pilot will have to fly at a bearing of 275 degrees to return from point C back to point A.