A person walks 25.0° north of east for 4.00 km. How far would the person walk due north and due east to arrive at the same location?
4*sin(25°) should be the distance north.
4*cos(25°) should be the distance east.
ah you're a life saver! :)
To find the distance that the person would have to walk due north and due east to arrive at the same location, we need to break down the initial displacement into its north and east components.
Given that the person walks 25.0° north of east for 4.00 km, we can use trigonometry to find the north and east components.
The north component, N, can be found using the equation N = displacement * sin(angle):
N = 4.00 km * sin(25.0°) = 4.00 km * 0.42262 = 1.69048 km
Similarly, the east component, E, can be found using the equation E = displacement * cos(angle):
E = 4.00 km * cos(25.0°) = 4.00 km * 0.90631 = 3.62524 km
Now that we have the north and east components, we can find the distances due north and due east by taking the absolute values of these components:
Distance due north = |N| = |1.69048 km| = 1.69048 km
Distance due east = |E| = |3.62524 km| = 3.62524 km
Therefore, the person would need to walk approximately 1.69048 km due north and 3.62524 km due east to arrive at the same location as when they walked 25.0° north of east for 4.00 km.