Bundle: Physics For Scientists And Engineers With Modern Physics, Loose-leaf Version, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
10th Edition
ISBN: 9781337888585
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 4, Problem 36AP
A particle starts from the origin with velocity
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A particle is moving in three dimensions and its position vector is given by;
r(t) = (4t² + 1.7t) î + (1.5t − 2.1)ĵ + (2.7t³ + 2t) k
where r is in meters and t is in seconds. Determine the magnitude of the instantaneous velocity at t = 3s. Express your answer in units of m/s using one decimal
place.
Answer:
The equation r(t) = ( sin t)i + ( cos t)j + (t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors.
π
Then write the particle's velocity at t=
as a product of its speed and direction.
The velocity vector is v(t) = (i+j+ k.
Problem 2: The position of a particle is given by the following expression, where t is time
measured in seconds: r(t) = [(3.65 m/s?)f²]į+ (-4.23 m)j + [(4.48 m/s³)r*]k.
Part (a) What is the magnitude of the velocity of the particle, in m/s, at t = 0.00 s?
Part (b) What is the magnitude of the velocity of the particle, in m/s, at t = 1.65 s?
Part (c) What angle, in degrees, does the velocity of the particle make with the +z axis at t =
1.65 s?
Part (d) What is the magnitude of the average velocity, in m/s, betweent = 0.00 s and t = 1.65
s?
Part (e) What angle, in degrees, does the average velocity between t = 0.00 s and t = 1.65 s
make with the z axis?
Chapter 4 Solutions
Bundle: Physics For Scientists And Engineers With Modern Physics, Loose-leaf Version, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
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 - Suppose the position vector for a particle is...Ch. 4 - The coordinates of an object moving in the xy...Ch. 4 - The vector position of a particle varies in time...Ch. 4 - It is not possible to see very small objects, such...Ch. 4 - Review. A snowmobile is originally at the point...
Ch. 4 - In a local bar, a customer slides an empty beer...Ch. 4 - Mayan kings and many school sports teams are named...Ch. 4 - A projectile is fired in such a way that its...Ch. 4 - The speed of a projectile when it reaches its...Ch. 4 - Prob. 10PCh. 4 - A firefighter, a distance d from a burning...Ch. 4 - A basketball star covers 2.80 m horizontally in a...Ch. 4 - A student stands at the edge of a cliff and throws...Ch. 4 - Prob. 14PCh. 4 - A home run is hit in such a way that the baseball...Ch. 4 - Prob. 16PCh. 4 - A boy stands on a diving board and tosses a stone...Ch. 4 - In Example 4.6, we found the centripetal...Ch. 4 - The astronaut orbiting the Earth in Figure P4.19...Ch. 4 - An athlete swings a ball, connected to the end of...Ch. 4 - The athlete shown in Figure P4.21 rotates a...Ch. 4 - A tire 0.500 m in radius rotates at a constant...Ch. 4 - (a) Can a particle moving with instantaneous speed...Ch. 4 - A ball swings counterclockwise in a vertical...Ch. 4 - Prob. 25PCh. 4 - The pilot of an airplane notes that the compass...Ch. 4 - You are taking flying lessons from an experienced...Ch. 4 - A car travels due east with a speed of 50.0 km/h....Ch. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - A river flows with a steady speed v. A student...Ch. 4 - You are participating in a summer internship with...Ch. 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. 35APCh. 4 - A particle starts from the origin with velocity...Ch. 4 - Lisa in her Lamborghini accelerates at...Ch. 4 - A boy throws a stone horizontally from the top of...Ch. 4 - Why is the following situation impossible? Albert...Ch. 4 - As some molten metal splashes, one droplet flies...Ch. 4 - Prob. 41APCh. 4 - A pendulum with a cord of length r = 1.00 m swings...Ch. 4 - A spring cannon is located at the edge of a table...Ch. 4 - A projectile is launched from the point (x = 0, y...Ch. 4 - A fisherman sets out upstream on a river. His...Ch. 4 - An outfielder throws a baseball to his catcher in...Ch. 4 - Prob. 47APCh. 4 - You are on the Pirates of the Caribbean attraction...Ch. 4 - A skier leaves the ramp of a ski jump with a...Ch. 4 - A projectile is fired up an incline (incline angle...Ch. 4 - Two swimmers, Chris and Sarah, start together at...Ch. 4 - In the What If? section of Example 4.5, it was...Ch. 4 - A fireworks rocket explodes at height h, the peak...
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