(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
Explanation of Solution
Given info: The velocity of the boat in still water is
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
Conclusion:
Therefore, the vector diagram is shown in the figure 1 and the velocity of the boat relative to water is labelled as
(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
Explanation of Solution
Write the expression to find the magnitude of the resultant of two vectors
Here,
Substitute
Conclusion:
Therefore, the magnitude of the velocity of boat relative to the Earth is
(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
Explanation of Solution
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)
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
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)
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
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
Want to see more full solutions like this?
Chapter 20 Solutions
Connect Access Card for Physics of Everyday Phenomena
- (a) Using the information in the previous problem, what velocity do you need to escape the Milky Way galaxy from our present position? (b) Would you need to accelerate a spaceship to this speed relative to Earth?arrow_forwardAn observer sitting on a park bench watches a person walking behind a runner. Figure P4.72A is the motion diagram representing what this observer sees. To better reveal the changing distance between runner and walker, five observations (A through E) are shown on five separate lines in Figure P4.72B. To the observer on the bench, both the runner and the walker move to the right, and the gap between them widens. Draw the motion diagram of the runner from the reference frame of the walker. FIGURE P4.72arrow_forwardSuppose an astronaut is moving relative to Earth at a significant fraction of the speed of light. (a) Does he observe the rate of his to have slowed? (b) What change in the rate of earthbound does he see? (c) Does his ship seem to him to shorten? (d) What about the distance between two stars that lie in the direction of his motion? (e) Do he and an earthbound observer agree on his velocity relative to Earth?arrow_forward
- A river is moving east at 4 m/s. A boat starts from the dock heading 30 north of west at 7 m/s. If the river is 1800 m wide, (a) what is the velocity of the boat with respect to Earth and (b) how long does it take the boat to cross the river?arrow_forwardAn experimentalist in a laboratory finds that a particle has a helical path. The position of this particle in the laboratory frame is given by r(t)=Rcost+Rsint+vztk where R, vz, and are constants. A moving frame has velocity (vM)L=vzk relative to the laboratory frame. a. What is the path of the particle in the moving frame? b. What is the velocity of the particle as a function of time relative to the moving frame? c. What is the acceleration of the particle in each frame? d. How should the acceleration in each frame be related? Does your answer to part (c) make sense? Explain.arrow_forwardA chameleon is resting quietly on a lanai screen, waiting for an insect to come by. Assume the origin of a Cartesian coordinate system at the lower left-hand corner of the screen and the horizontal direction to the right as the +x -direction. If its coordinates are (2.000 m, 1.000 m), (a) how far is it from the corner of the screen? (b) What is its location in polar coordinates?arrow_forward
- After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of time is given by v=1.2i9.8tj where v is in meters per second and t is in seconds. The balls displacement away from the edge of the table, during the time interval of 0.380 s for which the ball is in flight, is given by r=00.3803vdt To perform the integral, you can use the calculus theorem [A+Bf(x)]dx=Adx+Bf(x)dx You can think of the units and unit vectors as constants, represented by A and B. Perform the integration to calculate the displacement of the ball from the edge of the table at 0.380 s.arrow_forwardTwo birds begin next to each other and then fly through the air at the same elevation above level ground at 22.5 m/s. One flies northeast, and the other flies northwest. After flying for 10.5 s, what is the distance between them? Ignore the curvature of the Earth.arrow_forwardThe water in a river flows uniformly at a constant speed of 2.50 m/s between parallel banks 80.0 m apart. You are to deliver a package directly across the river, but you can swim only at 1.50 m/s. (a) If you choose to minimize the time you spend in the water, in what direction should you head? (b) How far downstream will you be carried? (c) If you choose to minimize the distance downstream that the river carries you, in what direction should you head? (d) How far downstream will you be carried?arrow_forward
- (a) A jet airplane flying from Darwin, Australia, has an air speed of 260 m/s in a direction 5.0° south of west. It is in the jet stream, which is blowing at 35.0 m/s in a direction 15° south of east. What is the velocity of the airplane relative to the Earth? (b) Discuss whether your answers are consistent with your expectations for the effect of the wind on the plane's path.arrow_forwardOne strategy in a snowball fight is to throw a snowball at a high angle over level ground. Then, while your opponent is watching that snowball, you throw a second one at a low angle timed to arrive before or at the same time as the first one. Assume both snowballs are thrown with a speed of 25.0 m/s. The first is thrown at an angle of 70.0 with respect to the horizontal. (a) At what angle should the second snowball be thrown to arrive at the same point as the first? (b) How many seconds later should the second snowball be thrown after the first for both to arrive at the same time?arrow_forwardOne strategy in a snowball fight is to throw a snowball at a high angle over level ground. Then, while your opponent is watching that snowball, you throw a second one at a low angle timed to arrive before or at the same time as the first one. Assume both snowballs are thrown with a speed of 25.0 m/s. The first is thrown at an angle of 70.0 with respect to the horizontal. (a) At what angle should the second snowball be thrown to arrive at the same point as the first? (b) How many seconds later should the second snowball be thrown after the first for both to arrive at the same time?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning