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

Answer:

B) 40 km West

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