Question

A mountain climbing expendition establishes a base camp and two intermediate camps ,A and B and a base camp .camp A is 11200 m east and 3200m above base camp .camp B is 8400 m east of and 1700 m higher than camp A.Determine the diaplacement between base camp amd camp B

Answer 1

→Suppose the base camp is at origin (0,0)

We consider the East as positive X axis and upward direction as Y axis.

I will mention distances with kilometers

→Camp A is 11.2 km east (11200m) and 3.2 km (3200m) above base camp.

So, coordinates of A : (11.2,3.2)

→Camp B is 8.4 km east and 1.7 km higher than camp A.

So, camp B is (8.4+11.2) km east of and (1.7+3.2) km higher than base camp.

So, coordinates of B :
(8.4+11.2, 1.7+3.2)
= (19.6, 4.9)


→ Now,
Coordinates of base camp: (0,0)
Coordinates of Camp B : (19.6,4.9) km

The straight line distance between them will give us the Displacement.

So, by Distance Formula of Coordinate Geometry,

Displacement
= √[ (19.6-0)² + (4.9-0)² ]
= √[ 384.16 + 24.01 ]
= √408.17
≈ 20.203 km
≈ 20.2 km

So, the Displacement between base camp and camp B is approximately 20,200 metres