Question

A boat is traveling due east at $12m{s}^{-1}$. A flag on the boat flaps at ${53}^{}N$ of $W$. Another flag on the shore flaps due north.

• A. Speed of wind with respect to ground is $16m{s}^{-1}$
• B. Speed of wind with respect to ground is $20m{s}^{-1}$
• C. Speed of wind with respect to boat is $20m{s}^{-1}$
• D. Speed of wind with respect to boat is $16m{s}^{-1}$

Answer 1

Answer: (A), (C)

The correct options are
A Speed of wind with respect to ground is $16m{s}^{-1}$
C Speed of wind with respect to boat is $20m{s}^{-1}$

Where,

$V_w=$ Velocity of wind

$V_b=$ Velocity of boat

$V_{wb}=$ Velocity of wind w.r. $+$ boat.

From figure, $\tan 53=\frac{4}{3}=\frac{V_w}{V_b}$

$\Rightarrow V_w=\frac{4\times 12}{3}=16m/s$

$V_{wb}=\sqrt{V_w^2+V_b^2}=20m/s$