Question
A steam boat goes across a lake up to a distance of 1200 meter and comes back. There is a uniform wind blowing with velocity $v$ so as to help the onward journey and to impede the journey back. If the uniform speed of launch of the boat is $5{\text{ }ms}^{- 1}$ and total time take by the boat in going and coming back is 500 s, the velocity $v$ of the wind blow is
Options
Solution
Sol. Key concept: Total journey time with different onward and return speeds.
In the intended model, the effective speeds are 5 + v and 5 − v. Each leg is 1200 m long, and the total time is 500 s.
$$\frac{1200}{5 + v} + \frac{1200}{5 - v} = 500$$
$$\frac{12000}{25 - v^{2}} = 500\ \ \Rightarrow \ \ \ v^{2} = 1$$
Taking the positive speed gives v = 1.0 m s⁻¹, option (c). The two times are 200 s and 300 s.
Correction / clarification: The direct addition/subtraction model is exact for a boat in a uniform water current. Real wind does not generally add its speed directly to a powered boat’s speed; the printed wind wording is an idealization.
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