Question

A man can swim at the rate of 5km/h in still water.A 1km wide river flows at the rate of 3 km/h.The man wishes to swim across the river directly opposite to the starting point.
a)Along what direction must the man swim?
b)What shoukd be hus resultant velocity?
c)How much time will he take to cross the river ?

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Answer 1

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The velocity of man with respect to river(${V}_{mR}$ )= 5km/h, this is greater than the river flow velocity, therefore, he can cross the river directly (along the shortest path).The angle of must be

a) $\theta$$\implies$$\large\frac{\pi}{2} + {\sin}^{-1} \frac{{V}_{r}}{{V}_{mR}}$

90°+ $\large{\sin}^{-1} \frac{{V}_{r}}{{V}_{mR}}$

$\implies$ 90° +37°

$\large\implies$ $\large{\boxed{\boxed{127°}}}$ w.r.t the river flow of 37°w.r.t perpendicular in backward direction

b) Resultant Velocity will be

${V}_{m}$$\sqrt{{{v}^{2}}_{mR}-{{v}^{2}}_{R}}$

$\implies$ $\sqrt{{5}^{2} - {3}^{2} }$

$\large\implies$ $\large{\boxed{\boxed{4}}}$

Along the direction perpendicular to the river flow.

c) Time taken to cross the t = $\large\frac{d}{\sqrt{{{v}^{2}}_{mR}-{{v}^{2}}_{R}}}$

$\implies$ $\large\frac{1}{4}$ hrs

$\large\implies$ $\large{\boxed{\boxed{15min}}}$

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Answer 2

check the attachment ❣️