Question

Two ships leave a port from a point at the same time. One goes with a velocity of $3km/h$ along North-East making an angle of $45^{\circ }$ with East direction and the other travels with a velocity of $4km/h$ along South-East making an angle of $15^{\circ }$ with East direction. Then, the distance between the ships at the end of two hours is

• A. $2\sqrt{13}$
• B. $\sqrt{13}$
• C. $5$
• D. $10$

Answer 1

Answer: (A)

Distance travelled by ship $OA$ direction in $2h$ is $6km$ and $OB$ direction in $2h138km$. $A{B}^2=O{A}^2+O{B}^2-20AOB\cos \angle AOB$
$A{B}^2=(6{)}^2+(8{)}^2-2\times 6\times 8\cos 60^{\circ }$
$A{B}^2=36+64-2\times 6\times 8\times \frac{1}{2}$

$AB=\sqrt{100-48}=\sqrt{52}$
$AB=2\sqrt{13}$