A plane flies 150km due south and then 150km on a bearing of 45 degrees Celsius. With repeat to it initial position, find
a. How far south the plane is
b. how far east the plane is is
c. It bearing
d. How far way it is
"45 degrees Celsius", huh?
We expect directions, not temperature. Please correct.
Lmao, Celsius?
To solve this problem, we need to break down the given information step by step.
a. How far south the plane is:
The plane flies 150km due south. This means it travels straight down on the map. Therefore, the answer is 150km.
b. How far east the plane is:
The plane flies 150km on a bearing of 45 degrees Celsius. To determine how far east it is, we need to find the east component of the displacement. The bearing of 45 degrees is measured clockwise from the north direction. Since we are given a bearing, we can use trigonometry to find the east component.
To calculate the east component, we use the sine function because the angle is between the hypotenuse (150km) and the adjacent side (which represents the east component).
East component = 150km * sin(45 degrees)
Using a calculator, sin(45 degrees) ≈ 0.7071
East component ≈ 150km * 0.7071 ≈ 106.065 km
Therefore, the plane is approximately 106.065 km east.
c. The bearing:
The bearing is given as 45 degrees Celsius. However, bear in mind that bearings are usually measured in degrees, not Celsius. Assuming that the bearing is indeed measured in degrees, we can conclude that the plane is traveling at an angle of 45 degrees clockwise from the north direction.
d. How far away it is:
To find the distance from the starting point to the current position (the displacement), we can use the Pythagorean theorem since we have a right triangle formed by the south component (150km) and east component (approximately 106.065 km).
Distance = √((south component)^2 + (east component)^2)
Distance = √((150km)^2 + (106.065km)^2)
Distance ≈ √(22500km^2 + 11246.56km^2)
Distance ≈ √33746.56km^2
Distance ≈ 183.722 km
Therefore, the plane is approximately 183.722 km away from its initial position.