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A man at point A directs his rowboat due north toward point B, straight across a river of width 100 m. The river current is due east. The man starts across, rowing steadily at 0.75 m/s and reaches the other side of the river at point C, 150 m downstream from his starting point. While the man is crossing the river, what is his velocity relative to the shore?

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Answer:

1.35208 m/s

Explanation:

Speed of the boat = 0.75 m/s

Distance between the shores = 100 m

Time = Distance / Speed

[tex]Time=\frac{100}{0.75}=133.33\ s[/tex]

Time taken by the boat to get across is 133.33 seconds

Point C is 150 m from B

Speed = Distance / Time

[tex]Speed=\frac{150}{\frac{100}{0.75}}=1.125\ m/s[/tex]

Velocity of the water is 1.125 m/s

From Pythagoras theorem

[tex]c=\sqrt{0.75^2+1.125^2}\\\Rightarrow c=1.35208\ m/s[/tex]

So, the man's velocity relative to the shore is 1.35208 m/s

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