
(a)
To draw the vector diagram of motion of a boat across stream and the velocity of the boat relative to water.
(a)

Answer to Problem 1SP
The vector diagram is shown in the figure 1 and the velocity of the boat relative to water is labelled as vsum.
Explanation of Solution
Given info: The velocity of the boat in still water is 7 m/s. The velocity of the stream is 3 m/s and the width of the stream is 28 m.
Following figure gives the diagram of the vector form of the motion of boat across the figure.
Figure 1
The figure 1 shows the velocity of water as vw and the velocity of the boat as vb. The resultant of the two vectors gives the velocity of the boat relative to water is labelled as vsum.
Conclusion:
Therefore, the vector diagram is shown in the figure 1 and the velocity of the boat relative to water is labelled as vsum.
(b)
To determine 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 7.6 m/s.
Explanation of Solution
Write the expression to find the magnitude of the resultant of two vectors vw and vb using Pythagorean Theorem.
vsum=√v2b+v2w
Here,
vsum is the velocity of the boat relative to water
vb is the velocity of the boat
vw is the velocity of water
Substitute 7 m/s for vb and 3 m/s for vw in the above equation.
vsum=√(7 m/s)2+(3 m/s)2=7.6 m/s
Conclusion:
Therefore, the magnitude of the velocity of boat relative to the Earth is 7.6 m/s.
(c)
To determine 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 4 s.
Explanation of Solution
Write the expression for the time taken for boat to cross the stream.
t=dv
Here,
d is the width of the stream
v is the velocity of the boat
t is the time taken
Substitute 28 m for d and 7 m/s for v in the above equation.
t=28 m7 m/s=4 s
Conclusion:
Therefore, the time taken for the boat to cross the stream is 4 s.
(d)
To determine 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 12 m.
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.
d=vt
Here,
d is the distance of the between the starting and ending point
v is the velocity of the water
t is the time taken
Substitute 4 s for t and 3m/s for v in the above equation.
d=(3m/s)(4 s)=12 m
Conclusion:
Therefore, the distance from starting point till the ending point along the downward flow of the stream is 12 m.
(e)
To determine the distance travelled by the boat before reaching the opposite bank.
(e)

Answer to Problem 1SP
The distance travelled by the boat before reaching the opposite bank is 30.5 m.
Explanation of Solution
Write the expression to find the magnitude of the resultant of two vectors dw and db using Pythagorean Theorem.
dsum=√d2b+d2w
Here,
dsum is the distance travelled by the boat before reaching the opposite bank
db is the distance travelled by the boat from starting to ending point along the river
dw is the width of the stream
Substitute 12 m for db and 28 m for dw in the above equation.
vsum=√(12 m)2+(28 m)2=30.5 m
Conclusion:
Therefore, the distance travelled by the boat before reaching the opposite bank is 30.5 m.
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Chapter 20 Solutions
Physics of Everyday Phenomena
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