SATHEE: Kinematics Question 526

Kinematics Question 526

Question: An aeroplane is to go along straight line from $A$ to $B$ , am back again. The relative speed with respect to wind it’s $V$ The wind blows perpendicular to line AB with speed v The distance between $A$ and $B$ it’s $l$ . The total time for round trip it’s

Options:

A) $\frac{2 ℓ}{\sqrt{V^{2} - v^{2}}}$

B) $\frac{2 v ℓ}{V^{2} - v^{2}}$

C) $\frac{2 V ℓ}{V^{2} - v^{2}}$

D) $\frac{2 ℓ}{\sqrt{V^{2} + v^{2}}}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] For no drift: $V \sin θ = v$

$\sin θ = \frac{v}{V}$

$∴ t = t_{A B} + t_{B A}$

$t = \frac{2 ℓ}{V \cos θ} = \frac{2 ℓ}{V \sqrt{1 - \frac{v^{2}}{V^{2}}}} \Rightarrow t = \frac{2 ℓ}{\sqrt{V^{2} - v^{2}}}$

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Kinematics Question 526

Question: An aeroplane is to go along straight line from A to B , am back again. The relative speed with respect to wind it’s V The wind blows perpendicular to line AB with speed v The distance between A and B it’s l . The total time for round trip it’s

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Question: An aeroplane is to go along straight line from $A$ to $B$ , am back again. The relative speed with respect to wind it’s $V$ The wind blows perpendicular to line AB with speed v The distance between $A$ and $B$ it’s $l$ . The total time for round trip it’s