Question

A sailboat sails 5 km east, 3 $\sqrt{2}$ km northeast and then an additional 3$\sqrt{5}$ km distance in an unknown direction. Its final position is $2$ km directly east of the starting point. If the direction of the third part of the journey is at an angle $ta{n}^{-1}\left(n\right)$ ( < ${90}^o$)with north, find $n$.

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

Answer: (C)

$2$

In the first part of the journey, the sailboat travels a distance of $5㎞$ in the east direction.

In the second part of the journey, it travels $3\sqrt{2}㎞$ in the northeast direction, i.e. $3$ kilometers each in north and east direction.

Thus the distance traveled so far is 8 kilometers in east direction and 3 kilometers in the north direction.

In the third part of the journey, it travels a distance of $3\sqrt{5}km$ in an unknown direction, but at the end, it reaches a spot such that is $2km$ to the east of the starting point.

$\therefore$ The boat travels 3 kilometers south and 6 kilometers west.

Constructing a triangle with sides $3,3\sqrt{2},3\sqrt{5}$

Hence the angle which it makes with north direction ${tan}^{-1}\left(2\right)$.

$\therefore$ n=2