Ludo walks so that she ends up being 40km and 25km east of her starting point.What is the bearing on which she has walked?
Without specifying a particular reference direction or landmark, it is impossible to determine the bearing on which Ludo has walked. Bearing is a measure of direction relative to a fixed reference point, usually true north or magnetic north. Additionally, the given information does not describe a specific path or direction, but rather the net displacement from the starting point. Therefore, different paths with different bearings could result in the same 40km east and 25km north displacement.
A plane flies for 150km on a bearing of 030degree and then for 259km on a bearing of 075degrees.
How far north has it travelled?
To find how far north the plane has traveled, we need to add up the north-south components of its two legs, which are opposite directions (180 degrees apart) to each other.
The first leg on a bearing of 030 degrees means that the angle between the plane's path and the northern axis (oriented towards the top of a map) is 90 - 30 = 60 degrees. Using trigonometry, the north-south component of this leg is 150 * sin(60) = 129.9 km north (rounded to one decimal place).
The second leg on a bearing of 075 degrees means that the angle between the plane's path and the northern axis is 90 - 75 = 15 degrees. Using trigonometry, the north-south component of this leg is 259 * sin(15) = 67.3 km north (rounded to one decimal place).
Therefore, the total northward distance traveled is 129.9 + 67.3 = 197.2 km north (rounded to one decimal place).
A plane flies for 150km on a bearing of 030degree and then for 259km on a bearing of 075degrees.
How far east has it travelled?
To find how far east the plane has traveled, we need to add up the east-west components of its two legs, which are perpendicular to each other.
The first leg on a bearing of 030 degrees means that the angle between the plane's path and the eastern axis (oriented towards the right of a map) is 30 degrees. Using trigonometry, the east-west component of this leg is 150 * cos(30) = 129.9 km east (rounded to one decimal place).
The second leg on a bearing of 075 degrees means that the angle between the plane's path and the eastern axis is 15 degrees (since 075 is 90 degrees minus 15 degrees). Using trigonometry, the east-west component of this leg is 259 * cos(15) = 247.5 km east (rounded to one decimal place).
Therefore, the total eastward distance traveled is 129.9 + 247.5 = 377.4 km east (rounded to one decimal place).
A plane flies for 150km on a bearing of 030degree and then for 259km on a bearing of 075degrees. Draw an illustration for the provided information.
What is it's bearing from it's starting point?
Here's an illustration of the plane's path:
```
Start A
o------|------------------->
150km 259km
030° 075°
B C
```
The plane starts at point A and flies 150 km on a bearing of 030 degrees to point B, then turns to a bearing of 075 degrees and flies 259 km to point C.
To find the bearing of the plane from its starting point, we need to find the angle between the plane's path and a line pointing due north (i.e. the 0 degree reference). One way to do this is to use the east and north components of the total displacement, which we can find by adding up the components of each leg:
East displacement = 129.9 km + 247.5 km = 377.4 km
North displacement = 129.9 km + 67.3 km = 197.2 km
The angle between this displacement vector and due north is given by:
tan θ = (East displacement) / (North displacement)
θ = atan(377.4 km / 197.2 km)
θ = 63.6 degrees (rounded to one decimal place)
Therefore, the bearing of the plane from its starting point is 090 + 63.6 = 153.6 degrees (rounded to one decimal place). This means the plane is headed southeast from its starting point.