QUESTION

# If the speed of a swimmer in still water is $9\text{ km/h}$ . Find the downstream speed of the swimmer when the river is flowing with a speed of $6\text{ km/h}$ ?(a) $15\text{ km/h}$(b) $18\text{ km/h}$(c) $3\text{ km/h}$(d) $12\text{ km/h}$

Hint:For solving this equation we will first understand how we can add two velocity vectors when they are parallel to each other. Then we can answer this question correctly.

Now, let $\overrightarrow{{{V}_{S}}}$ is the velocity vector of the swimmer velocity in still water, $\overrightarrow{{{V}_{W}}}$ is the velocity vector of the flow of the river and $\overrightarrow{{{V}_{D}}}$ is the downstream velocity vector. Then,
$\overrightarrow{{{V}_{D}}}=\overrightarrow{{{V}_{S}}}+\overrightarrow{{{V}_{W}}}$
Now, as we know that $\overrightarrow{{{V}_{S}}}$ is parallel to $\overrightarrow{{{V}_{W}}}$ . Then magnitude of $\overrightarrow{{{V}_{D}}}$ = 9 + 6 = 15 km/h.