Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 2, Problem 22P
In the particle under constant acceleration model, we identify the variables and parameters vxi, vxf, ax, t, and xf − xi. Of the equations in the model. Equations 2.13–2.17, the first does not involve xf − xi, the second and third do not contain ax, the fourth omits vxf, and the last leaves out t. So, to complete the set, there should be an equation not involving vxi. Derive it from the others.
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As illustrated in the figure, a particle P moves on an x- y plane. In this motion, x( t) = 3 2 in meters and
a(y) = 4 m /s?. It is also known that the position and velocity component along the y axis both vanish.
Determine the speed as well as the x and y position of the particle at i = 3s. In your opinion, is the figure
correct? If not, explain why and sketch a correction.
Trajectory
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P
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In the vertical jump, an Kobe Bryant starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00 s in the air (their "hang time"). Treat Kobe as a particle and let ymax be his maximum height above the floor. Note: this isn't the entire story since Kobe can twist and curl up in the air, but then we can no longer treat him as a particle.
Hint: Find v0 to reach y_max in terms of g and y_max and recall the velocity at y_max is zero. Then find v1 to reach y_max/2 with the same kinematic equation. The time to reach y_max is obtained from v0=g (t), and the time to reach y_max/2 is given by v1-v0= -g(t1). Now, t1 is the time to reach y_max/2, and the quantity t-t1 is the time to go from y_max/2 to y_max. You want the ratio of (t-t1)/t1
Note from Asker: I am generally confused on how to manipulate the formulas, so if you could show every step that would be great, Thank You.
Part A
Part complete
To explain why…
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.
Chapter 2 Solutions
Physics for Scientists and Engineers with Modern Physics
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