Question

An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. he was supposed to travel due north for 5.4 km, but when the snow clears, he discovers that he actually traveled 8.1 km at 47o north of due east. (a) how far and (b) in what direction (south of due west) must he now travel to reach base camp?

Answer 1

Actual displacement that he required to move

$d_1 = 5.4 km$ towards North

Displacement that he moved due to snow is

$d_2 = 8.1 km$ at 47 degree North of East

now in vector component form we can say

$d_1 = 5.4 \hat j$

$d_2 = 8.1 cos47 \hat i + 8.1 sin47 \hat j$

$d_2 = 5.52 \hat i + 5.92 \hat j$

now the displacement that is more required to reach the destination is given as

$d = d_1 - d_2$

$d = 5.4\hat j - (5.52 \hat i + 5.92\hat j)$

$d = -5.52 \hat i - 0.52 \hat j$

so the magnitude of the displacement is given as

$d = \sqrt{5.52^2 + 0.52^2}$

$d = 5.54 km$

its direction is given as

$\theta = tan^{-1}\frac{0.52}{5.52} = 5.38 degree$

so it is 5.54 km towards 5.38 degree North of West.