(a)
The vector diagram to o the velocity of the boat relative to Earth.
(a)
Answer to Problem 1SP
The vector diagram is shown is
and the velocity of the boat relative to water is labelled as
Explanation of Solution
Vector diagram are used to describe the velocity of a moving object during its motion. In a vector diagram, the magnitude of the vector is represented by the length of the vector arrow and the direction is given by the arrow head.
Figure 1
The vector diagram showing the motion of the boat is drawn in figure 1. The velocity of the boat relative to the water is represented by
Conclusion:
Therefore, the vector diagram is shown in the figure 1 and the velocity of the boat relative to water is labelled as
(b)
The magnitude of the velocity of boat relative to the Earth.
(b)
Answer to Problem 1SP
The magnitude of the velocity of boat relative to the Earth is
Explanation of Solution
Given info: The velocity of the boat relative to water is
Write the expression to find the magnitude of the velocity of boat relative to Earth according to Pythagorean Theorem.
Here,
Substitute
Conclusion:
Therefore, the magnitude of the velocity of boat relative to the Earth is
(c)
The time taken for the boat to cross the stream.
(c)
Answer to Problem 1SP
The time taken for the boat to cross the stream is
Explanation of Solution
Given info: The width of the stream is
Write the expression for the time taken for boat to cross the stream.
Here,
Substitute
Conclusion:
Therefore, the time taken for the boat to cross the stream is
(d)
The distance from starting point till the ending point along the downward flow of the stream.
(d)
Answer to Problem 1SP
The distance from starting point till the ending point along the downward flow of the stream is
Explanation of Solution
Write the expression to find the distance of the between the starting and ending point of the boat along the flow of the stream.
Here,
Substitute
Conclusion:
Therefore, the distance from starting point till the ending point along the downward flow of the stream is
(e)
The distance travelled by the boat in reaching the opposite bank.
(e)
Answer to Problem 1SP
The distance travelled by the boat in reaching the opposite bank is
Explanation of Solution
Write the expression to find the magnitude of the resultant of two vectors
Here,
Substitute
Conclusion:
Therefore, the distance travelled by the boat before reaching the opposite bank is
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