A boat problem (I'm not sure what to classify it under)

Classical Mechanics Level 2

A boat is travelling in a river at speed v 1 v_1 relative to still water, with the speed of the water current as v 2 v_2 . When the boat steers perpendicularly to the bank at speed v 1 v_1 , it reaches the opposite bank at time t 1 t_1 . When the boat steers at an angle upstream such that it will reach directly opposite of its starting point with the same speed, the time taken is t 2 t_2 . What is the ratio of v 1 v_1 to v 2 v_2 ? \\ \\ Assume drag is negligible.

t 1 t 2 2 − t 1 2 \frac{t_1}{\sqrt{{t_2}^2-{t_1}^2}} t 2 t 2 2 + t 1 2 \frac{t_2}{\sqrt{{t_2}^2+{t_1}^2}} t 1 t 2 2 + t 1 2 \frac{t_1}{\sqrt{{t_2}^2+{t_1}^2}} t 2 t 2 2 − t 1 2 \frac{t_2}{\sqrt{{t_2}^2-{t_1}^2}}

Klement Chua by Klement Chua , 15, Singapore

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