
A boat travels from the south bank to the north bank of a river with a maximum speed of . A river current flows from west to east with a speed of . Find the angle with which the boat should be steered to arrive at a point opposite to the point of start.
(a)
(b)
(c)
(d)
Answer
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Hint: In order to answer this question, we have to calculate the angle with which the boat should be steered to arrive at a point opposite to the point of start, we will first draw a diagram respect to the given problem and then we will take sine angle to solve for it.
Complete step by step answer:
Velocity of the boat
And, the velocity of the river from west to east
So, according to the question:
In the above figure, the angle is .
So, as the angle with which the boat should be steered to arrive at a point opposite to the point of start is as:
.
Therefore, the angle with which the boat should be steered to arrive at a point opposite to the point of start is .
Hence, the correct option is (b).
Note: As we know, the given question is related to the river boat topic, so to solve river boat problems, we need to understand two concepts: The speed of a boat relative to the water is equal to the speed of the boat in still water.
Complete step by step answer:
Velocity of the boat
And, the velocity of the river from west to east
So, according to the question:

In the above figure, the angle is
So, as the angle with which the boat should be steered to arrive at a point opposite to the point of start is as:
Therefore, the angle with which the boat should be steered to arrive at a point opposite to the point of start is
Hence, the correct option is (b).
Note: As we know, the given question is related to the river boat topic, so to solve river boat problems, we need to understand two concepts: The speed of a boat relative to the water is equal to the speed of the boat in still water.
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