a swimmer can swim at a speed of 0.6m/s with respect to water . she wants to cross a river which is 50 m wide and has a water current of 0.36 m/s . if she wants to reach on the other bank of the point directly opposite to her starting point in which direction she must swim
Answers
Answer:
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The swimmer should travel in the direction opposite to the flow of river at an angle of 53° with respect to the horizontal.
Given:
Speed of swimmer
Width of the river
Speed of the water in river
To find:
The direction in which he swimmer should swim in order to reach the exact opposite point.
Solution:
From the figure, lets assume that the swimmer starts swimming from with a speed . According to the question, the swimmer wants to reach the point but, as we know, the river is flowing with a velocity .
If the swimmer swims in the direction , he will lose the trajectory of the path and miss the point by flowing in the direction of the river.
To cover this gap, the swimmer needs to swim in the direction opposite to the flow of the river at an angle θ with the horizontal.
Lets assume, the target point of the swimmer be the point which makes an angle θ with the river. Hence, with the presence of the flow of river, swimmer reaches the required point .
Now,
In Δ, we have, ∠ θ, Hence,
θ
θ
θ
Hence,
θ
θ
The swimmer needs to travel with an angle of with respect to the origin with the horizontal.
Final answer:
Hence, the swimmer should travel in the direction opposite to the flow of river at an angle of 53° with respect to the horizontal.