Question

41. City A lies 30 km directly south of city B. A bus, beginning at city A travels 50 km at 37° north of east to reach city C. How far and in what direction must the bus go from city C to reach city B? A) 20 km, west B) 40 km, west C) 80 km, west D) 40 km, east E) 80 km, east

Answer 1

B) 40 km West

Step-by-step explanation:

Let position of B is origin so with respect of City B the position of A is given as

`r_A = 30 km` south of city B

now Bus starts from City A and travels a distance of 50 km at 37 degree North of East to reach city C

so it is

`r_(CA) = 50(cos37\hat i + sin37 \hat j)`

`r_(CA) = 40\hat i + 30\hat j`

now the position of C is given with respect to A

in order to find the position of C with respect to B we can say

`r_C = r_(CA) + r_A`

`r_C = 40\hat i + 30\hat j + (-30 \hat j)`

`r_C = 40 \hat i`

so in order to reach at city B from city C bus has to travel 40 km towards West