Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
9th Edition
ISBN: 9781305372337
Author: Raymond A. Serway | John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 4, Problem 5P
(a)
To determine
The vector expression for the ball’s position as a function of time, using the unit vectors
(b)
To determine
The velocity vector
(c)
To determine
The acceleration vector
(d)
To determine
The position vector, velocity vector and acceleration vector at time
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by
x = 17.2t
and
y = 4.16t − 4.90t2,
where x and y are in meters and t is in seconds.
(a) Write a vector expression for the ball's position as a function of time, using the unit vectors î and ĵ. (Give the answer in terms of t.) =
m
By taking derivatives, do the following. (Give the answers in terms of t.)
(b) obtain the expression for the velocity vector as a function of time =
m/s(c) obtain the expression for the acceleration vector as a function of time =
m/s2(d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 3.18 s.
=
m
=
m/s
=
m/s2
A space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 - 2.1t , where x and y are in meters and t is in seconds. write a vector expression for the ball's position as a function of time.
A golf ball is hit off a tee at the edge of a cliff. Its x and y
coordinates as functions of time are given by the following
expressions:
2.
x = (18.0 m/s)t
and
y = (4.00 m/s)t – (4.90 m/s²) t²
(a) Write a vector expression for the ball's position as a
function of time, using the unit vectors i and j. By taking
derivatives, obtain expressions for (b) the velocity vector v
as a function of time and (c) the acceleration vector a as a
function of time. Next use unit-vector notation to write ex-
pressions for (d) the position, (e) the velocity, and (f) the
acceleration of the golf ball, all at t = 3.00 s.
Chapter 4 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
Ch. 4.1 - Consider the following controls in an automobile...Ch. 4.3 - (i) As a projectile thrown at an upward angle...Ch. 4.3 - Rank the launch angles for the five paths in...Ch. 4.4 - A particle moves in a circular path of radius r...Ch. 4.5 - A particle moves along a path, and its speed...Ch. 4 - Prob. 1OQCh. 4 - Entering his dorm room, a student tosses his book...Ch. 4 - A student throws a heavy red ball horizontally...Ch. 4 - Prob. 4OQCh. 4 - Does a car moving around a circular track with...
Ch. 4 - An astronaut hits a golf ball on the Moon. Which...Ch. 4 - Prob. 7OQCh. 4 - Prob. 8OQCh. 4 - A sailor drops a wrench from the top of a...Ch. 4 - A baseball is thrown from the outfield toward the...Ch. 4 - A set of keys on the end of a string is swung...Ch. 4 - A rubber stopper on the end of a string is swung...Ch. 4 - Prob. 13OQCh. 4 - A spacecraft drifts through space at a constant...Ch. 4 - Prob. 2CQCh. 4 - Prob. 3CQCh. 4 - Describe how a driver can steer a car traveling at...Ch. 4 - A projectile is launched at some angle to the...Ch. 4 - Construct motion diagrams showing the velocity and...Ch. 4 - Explain whether or not the following particles...Ch. 4 - Prob. 1PCh. 4 - When the Sun is directly overhead, a hawk dives...Ch. 4 - Suppose the position vector for a particle is...Ch. 4 - The coordinates of an object moving in the xy...Ch. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - The vector position of a particle varies in time...Ch. 4 - It is not possible to see very small objects, such...Ch. 4 - Prob. 9PCh. 4 - Review. A snowmobile is originally at the point...Ch. 4 - Mayan kings and many school sports teams are named...Ch. 4 - Prob. 12PCh. 4 - In a local bar, a customer slides an empty beer...Ch. 4 - Prob. 14PCh. 4 - A projectile is fired in such a way that its...Ch. 4 - Prob. 16PCh. 4 - Chinook salmon are able to move through water...Ch. 4 - Prob. 18PCh. 4 - The speed of a projectile when it reaches its...Ch. 4 - Prob. 20PCh. 4 - A firefighter, a distance d from a burning...Ch. 4 - Prob. 22PCh. 4 - A placekicker must kick a football from a point...Ch. 4 - A basketball star covers 2.80 m horizontally in a...Ch. 4 - A playground is on the flat roof of a city school,...Ch. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - A student stands at the edge of a cliff and throws...Ch. 4 - Prob. 30PCh. 4 - A boy stands on a diving board and tosses a stone...Ch. 4 - A home run is hit in such a way that the baseball...Ch. 4 - The athlete shown in Figure P4.21 rotates a...Ch. 4 - In Example 4.6, we found the centripetal...Ch. 4 - Prob. 35PCh. 4 - A tire 0.500 m in radius rotates at a constant...Ch. 4 - Review. The 20-g centrifuge at NASAs Ames Research...Ch. 4 - An athlete swings a ball, connected to the end of...Ch. 4 - The astronaut orbiting the Earth in Figure P4.19...Ch. 4 - Figure P4.40 represents the total acceleration of...Ch. 4 - Prob. 41PCh. 4 - A ball swings counterclockwise in a vertical...Ch. 4 - (a) Can a particle moving with instantaneous speed...Ch. 4 - The pilot of an airplane notes that the compass...Ch. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - A police car traveling at 95.0 km/h is traveling...Ch. 4 - A car travels due east with a speed of 50.0 km/h....Ch. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - A river flows with a steady speed v. A student...Ch. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - A farm truck moves due east with a constant...Ch. 4 - A ball on the end of a string is whirled around in...Ch. 4 - Prob. 56APCh. 4 - Prob. 57APCh. 4 - A particle starts from the origin with velocity...Ch. 4 - Prob. 59APCh. 4 - Prob. 60APCh. 4 - Lisa in her Lamborghini accelerates at...Ch. 4 - A boy throws a stone horizontally from the top of...Ch. 4 - Prob. 63APCh. 4 - Prob. 64APCh. 4 - Prob. 65APCh. 4 - Prob. 66APCh. 4 - Why is the following situation impossible? Albert...Ch. 4 - As some molten metal splashes, one droplet flies...Ch. 4 - Prob. 69APCh. 4 - A pendulum with a cord of length r = 1.00 m swings...Ch. 4 - Prob. 71APCh. 4 - A projectile is launched from the point (x = 0, y...Ch. 4 - A spring cannon is located at the edge of a table...Ch. 4 - An outfielder throws a baseball to his catcher in...Ch. 4 - A World War II bomber flies horizontally over...Ch. 4 - Prob. 76APCh. 4 - Prob. 77APCh. 4 - Prob. 78APCh. 4 - A fisherman sets out upstream on a river. His...Ch. 4 - Prob. 80APCh. 4 - A skier leaves the ramp of a ski jump with a...Ch. 4 - Two swimmers, Chris and Sarah, start together at...Ch. 4 - Prob. 83CPCh. 4 - Prob. 84CPCh. 4 - Prob. 85CPCh. 4 - A projectile is fired up an incline (incline angle...Ch. 4 - A fireworks rocket explodes at height h, the peak...Ch. 4 - In the What If? section of Example 4.5, it was...Ch. 4 - Prob. 89CP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- What is the y component of the vector (3i8k) m/s? (a) 3 m/s (b) 8 m/s (c) 0 (d) 8 m/s (e) none of those answersarrow_forwardVector B has x, y, and z components of 4.00, 6.00, and 3.00 units, respectively. Calculate (a) the magnitude of B and (b) the angle that B makes with each coordinate axis.arrow_forwardThree displacement vectors of a croquet ball are shown in Figure P1.44, where |A|=20.0units, |B|=40.0units, and |C|=30.0units. Find (a) the resultant in unit-vector notation and (b) the magnitude and direction of the resultant displacement. Figure P1.44arrow_forward
- Vector A has x and y components of 8.70 cm and 15.0 cm, respectively; vector B has x and y components of 13.2 cm and 6.60 cm, respectively. If AB+3C=0, what are the components of C?arrow_forwardA hiker walks from (x1, y1) = (4.00 km. 3.00 km) to (x2, y2) = (3.00 km, 6.00 km), (a) What distance has the traveled? (b) The hiker desires to return to his starting point. In what direction should he go? (Give the angle with respect to due cast.) (See Sections 3.2 and 3.3.)arrow_forwardWhat is the y component of the vector (3i 8k) m/s? (a) 3 m/s (b) 8 m/s (c) 0 (d) 8 m/s (e) none of those answersarrow_forward
- A delivery man starts at the post office, chives 40 km north, then 20 km west, then 60 km northeast, and finally 50 km north to stop for lunch. Use a graphical method to find his net displacement vector.arrow_forwardFind the horizontal and vertical components of the 100-m displacement of a superhero who flies from the top of a tall building following the path shown in Figure P1.40. Figure P1.40arrow_forwardThe magnitudes of two vectors A and B are 12 units and 8 units, respectively. What are the largest and smallest possible values for the magnitude of the resultant vector R = A + B? (a) 14.4 and 4 (b) 12 and 8 (c) 20 and 4 (d) none of these.arrow_forward
- A vector points from the origin into the second quadrant of the xy plane. What can you conclude about its components? (a) Both components are positive. (b) The x component is positive, and the y component is negative. (c) The x component is negative, and the y component is positive. (d) Both components are negative. (e) More than one answer is possible.arrow_forwardAs it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 63.0° north of west with a speed of 40.2 km/h. (Let i represent east and j represent north.) (a) What is the unit-vector expression for the velocity of the hurricane? km/h i+ km/hi It maintains this velocity for 3.50 h, at which time the course of the hurricane suddenly shifts due north, and its speed slows to a constant 25.2 km/h. This new velocity is maintained for 1.50 h. (b) What is the unit-vector expression for the new velocity of the hurricane? km/h j km/h i+ (c) What is the unit-vector expression for the displacement of the hurricane during the first 3.50 h? km i+ km j (d) What is the unit-vector expression for the displacement of the hurricane during the latter 1.50 h? km i+ km j (e) How far from Grand Bahama is the eye 5.00 h after it passes over the island? kmarrow_forwardAn electron's position is given by r=(ti+t2j+2k) with t in seconds and r in meters. A)Determine the electron's velocity v(t) in unit vector notation. B)What is the magnitude of v(t) at t=2 s? C)What is the angle between v(t) and the unit vector ı ?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
College Physics
Physics
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Introduction to Vectors and Their Operations; Author: Professor Dave Explains;https://www.youtube.com/watch?v=KBSCMTYaH1s;License: Standard YouTube License, CC-BY