Question

A boat sails 2 km east, then 4km northeast and then in an unknown direction. Final position of the boat is 5 km east from starting point. Unknown displacement is

• A. 2.8 km, 3°26' with north towards east
• B. 3km 2°26' with east
• C. 3.5 kin, 2°30' with south towards west
• D. 1.81cm, 2°36' with north towards east.

Answer 1

Answer: (A)

2.8 km, 3°26' with north towards east

Answer 2

$\overrightarrow{S}$ = $\overrightarrow{S}$₁ + $\overrightarrow{S}$₂ + $\overrightarrow{S}$₃

5$\widehat{i}$ = 2$\widehat{i}$ + [(4 cos 45⁰)$\widehat{i}$ - (4 sin 45^o)$\widehat{j}$] + $\overrightarrow{S}$₃

i.e. $\overrightarrow{S}$₃ = (3$\widehat{i}$ - 2√2)$\widehat{i}$ + 2√2$\widehat{j}$

= 0.172$\widehat{i}$ + 2.828$\widehat{j}$

i.e., S₃ = $\sqrt{0.172^{2} + 2.828^{2}}$

= 2.8 km

and tan θ = 0.172/2.828 = 0.0608

or θ = tan^-1 0.0608

or θ = 3⁰ 26'