# Math Help - geometric vector force

A man can row a boat through still water at 4km/h. How long will it take him to cross an 18 m wide river flow at 2 km/h (a) by rowing at right angles to the current; (b) by rowing in a direction such that he lands directly opposite his starting point?

2. Originally Posted by bobby77
A man can row a boat through still water at 4km/h. How long will it take him to cross an 18 m wide river flow at 2 km/h (a) by rowing at right angles to the current; (b) by rowing in a direction such that he lands directly opposite his starting point?
The essence of the question is that your velocity relative to the ground is the sum of the velocities of the boat and the river.

Part (a)
You row at right angles. Hence your velocity across the river=4km/h
Time taken=.018km/(4km/h) = .0045h=16.2sec.

Part (b)
In this case you row at such an angle that the resultant of velocity along the river is zero.
Let you row at an angle $\alpha$with the land.
Then,
$4cos\alpha=2$
Velocity acros the river is $4sin\alpha=2\sqrt{3}$.
Hence time taken = $\frac{.018km}{2\sqrt{3}km/h}=23sec.$

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Malay