First slide

Projectile motion

Question

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

Difficult

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

$\frac{2 l}{\sqrt{V^{2} + v^{2}}}$

Solution

$For no drift: V \sin θ = v$
$\begin{array}{l} \sin θ = \frac{v}{V} ∴ t = t_{A B} + t_{B A} \\ t = \frac{2 ℓ}{V \cos θ} = \frac{2 ℓ}{V \sqrt{1 - \frac{v^{2}}{V^{2}}}} \Rightarrow t = \frac{2 ℓ}{\sqrt{V^{2} - v^{2}}} \end{array}$

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