Question

Hilary and Dale leave camp and go for a long hike. After going 7 km due east, they turn and go another 8 km in the direction 60 degrees north of east. They plan to return along a straight path. How far from camp are they at this point? Use an angle to describe the direction that Hilary and Dale should follow to reach their camp.

Answer 1

Explanation:

Given

First they travel 7 km east , then they go 8 km in direction 60^{\circ} north of east

Position vector of first point

`r_1=7\hat{i}`

`r_(21)=8cos60\hat{i}+8sin60\hat{j}`

`r_(21)=4\hat{i}+6.92\hat{j}`

Position vector of
`r_2` w.r.t to origin

`r_2=r_(21)+r_1`

`r_2=4\hat{i}+6.92\hat{j}+7\hat{i}`

`r_2=11\hat{i}+6.92\hat{j}`

magnitude of
`r_2` will give the distance they are from original point

`|r_2|=√(6.92^2+11^2)=13`

direction

`tan\theta =(y)/(x)=(6.92)/(11)`

`\theta =32.17^(\circ)` North of east