Question

Oasis B is a distance d = 9.0 km east of oasis A, along the x axis shown in the figure. A confused camel, intending to walk directly from A to B instead walks a distance W1 = 22 km west of due south by angle θ1 = 15.0°. It then walks a distance W2 = 30 km due north. If it is to then walk directly to B, (a) how far (in km) and (b) in what direction should it walk (relative to the positive direction of the x axis within the range (-180°, 180°])?

Answer 1

Actual displacement of the camel is,

S = 9 i

First displacement is,

s = 24 cos 15 (-j) + 24 sin 15 ( -i)

            = -23.18 j - 6.211 i

Second displacement is,

s ' = 31 j

Here, i , j are the unit vectors along east and north directions.

Need to calculate the third displacement s "

s + s' +s " = S

           s " = S - s - s '

                = 9i +23.18 j + 6.211 i -31 j

                = 15.211 i-7.82 j

Magnitude of s " = √ [ 15.211 ² + (-7.82) ² ]

                          = 17.1 km

Let s " makes an angle θ with east along south then,

tan θ = 7.82 / 15.211

       θ = 27.2 ^o