Concept explainers
(a)
The components of the acceleration of the fish.
(a)
Answer to Problem 9P
The horizontal component of acceleration for the fish is
Explanation of Solution
As per given condition in the problem, this case is related to constant acceleration
According to constant acceleration, motion in two dimensions can be modeled as two independent motions in each of the two perpendicular directions associated with the
At
At
Write the general expression for acceleration as.
Here,
Write the expression for acceleration in
Here,
Write the expression for acceleration in
Here,
Write the final expression for acceleration in
Here,
Conclusion:
Substitute
Substitute
Thus, the horizontal component of acceleration for the fish is
(b)
The direction of the acceleration with respect to unit vector.
(b)
Answer to Problem 9P
The direction of the net acceleration is
Explanation of Solution
Write the expression for direction of the acceleration of the fish as.
Here
Conclusion:
Substitute
The direction of the net acceleration is
Thus, the direction of the net acceleration from the positive
(c)
The direction and the position of the fish at constant acceleration in
(c)
Answer to Problem 9P
The
Explanation of Solution
The position vector
Write the expression for final position vector for horizontal component as.
Here,
Write the expression for final position vector as.
Here,
Write the expression for final position vector as.
Here,
Write the expression for final velocity at
Here,
Write the expression for direction of the velocity components at
Conclusion:
Substitute
Substitute
Thus, the position vector for the fish at
Substitute
Substitute
Substitute
Thus, the direction of the velocity component is
Want to see more full solutions like this?
Chapter 4 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
- A fish swimming in a horizontal plane has velocity v = (4.00 î + 1.00 j) m/s at a point in the ocean where the position relative to a certain rock is ï = (10.0 î – 4.00 j) m . After the fish swims with constant acceleration for 20.0 s, its velocity is v = (20.0 î – 5.00 j) m/s . 1. What are the components of the acceleration of the fish? 2. What is the direction of its acceleration with respect to unit vector î ? 3. If the fish maintains constant acceleration, where is it at t = 25.0 s and in what direction is it moving?arrow_forwardA fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (12.0 î − 2.60 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (25.0 î − 1.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = ay = (b) What is the direction of its acceleration with respect to unit vector î? Draw coordinate axes on a separate piece of paper, and then add the acceleration vector with its tail at the origin. Write the numerical values for the x and y components and then use this drawing to determine the angle.° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 28.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axisarrow_forwardA particle leaves the origin with initial velocity v⃗ o=12i^+12j^m/s , undergoing constant acceleration a⃗ =−1.0i^+0.28j^m/s2 . When does the particle cross the y�-axis?arrow_forward
- A fish swimming in a horizontal plane has velocity given by v i j i = 4ˆ + ˆ m/s at a point in theocean where the position relative to a certain rock is r i j i = 10ˆ − 4 ˆ m. After the fish swimswith constant acceleration for 20.0 s, its velocity is v i j = 20ˆ − 5 ˆ m/s.a) What are the components of the acceleration of the fish?b) What is the direction of its acceleration with respect to the unit vector along the x axis?c) If the fish maintains constant acceleration, where is it at t = 25.0 s and in what direction isit moving?arrow_forwardA fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (16.0 î − 3.20 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (21.0 î − 6.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 30.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axisarrow_forwardA fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (16.0 î − 3.20 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (21.0 î − 6.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 30.0 s? x = 542.5 Remember that you can treat the motions in the x and y directions separately. Each is then treated exactly as you would the one-dimensional case. m y = m In what direction is it moving? ° counterclockwise from the +x-axiarrow_forward
- A fish swimming in a horizontal plane has velocity v, = (4.00 î + 1.00 j) m/s at a point in the ocean where the position relative to a certain rock is ř = (12.0 î - 2.20 j) m. After the fish swims with constant acceleration for 15.0 s, its velocity is v = (25.0 î – 3.00 î) m/s. (a) What are the components of the acceleration of the fish? ax = |m/s² ay |m/s² (b) What is the direction of its acceleration with respect to unit vector î? counterclockwise from the +x-axis (c) If the fish maintains constant acceleration, where is it at t = 30.0 s? x3= m y = In what direction is it moving? counterclockwise from the +x-axisarrow_forwardThe position of a particle is: r(t) = [(4.62 m/s^2) t^2] i + (-3.38m) j + [(4.04 m/s^3) t^3] k What is the magnitude in m/s of the average velocity between t = 0 and t = 1.79s and what angle in degrees does the average velocity make between t = 0s and t = 1.79sarrow_forwardA fish swimming in a horizontal plane has velocity (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is ₁ = (15.0 î – 1.70 ĵ) m. After the fish swims with constant acceleration for 18.0 s, its velocity is = (24.0 î – 6.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? (b) What is the direction of its acceleration with respect to unit vector î? (c) If the fish maintains constant acceleration, where is it at t = 30.0 s? In what direction is it moving? Part 1 of 7 - Conceptualize The fish is speeding up and changing direction in a horizontal plane relative to a known position vector. We will write separate equations to describe the x and y components of its motion under constant acceleration. Part 2 of 7 - Categorize We will model the fish as an object under constant acceleration. We use the standard equations for two dimensional motion in the xy plane. We will use x and y subscripts for the components of position, velocity,…arrow_forward
- At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive ydirection and moves in the xy plane with a constant acceleration of (2.0i - 4.0j)m/s2. At the instant the x coordinate of the particle is 15 m, what is the speedof the particle?arrow_forwardA fish swimming in a horizontal plane has velocity v, = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is r, = (16.0 î – 1.60 j) m. After the fish swims %3D with constant acceleration for 15.0 s, its velocity is v = (17.0 î – 6.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? a. m/s2 = a, m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis (c) If the fish maintains constant acceleration, where is it at t = 28.0 s? X = y = In what direction is it moving? ° counterclockwise from the +x-axisarrow_forwardA fish swimming in a horizontal plane has velocity v, = (4.00 î + 1.00 j) m/s at a point in the ocean where the position relative to a certain rock is r = (12.0 î - 2.20 j) m. After the fish swims with constant acceleration for 15.0 s, its velocity is V = (25.0 î - 3.00 j) m/s. (a) What are the components of the acceleration of the fish? ax m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis (c) If the fish maintains constant acceleration, where is it at t = 30.0 s? y = In what direction is it moving? o counterclockwise from the +x-axisarrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON