Question

A plane flies from base camp to Lake A, 290 km away in the direction 20.0° north of east. After dropping off supplies it flies to Lake B, which is 180 km at 30.0° west of north from Lake A. Graphically determine the distance and direction from Lake B to the base camp. Distance and Direction?

Answer 1

the x componnet of plane along lake A is

Ax = A cos theta = 290 km cos 20 = 272.51 km

the y component is

Ay = A sin theta = 290 km sin 20 = 99.18 km

the y componnet of plane along lake B is

By = B cos theta = 180 km cos 30 = 155.8km

the x componnet of plane along lake B is

Bx =- B sin theta = -180 km sin 30 = -90km

A= Ax + Bx = 272.51 km-90 km=182.51 km

B = Ay + By = 99.18 km+155.8km =254.98 km

the distance and direction from Lake B to the base camp is

d = root A^2 + B^2 = roor (182.51 km)^2+ ( 254.98 km)^2 = 313.56 km

direction is

theta = tan^-1 ( 254.98 km/ 182.51 km) = 54.4 degree south of west