homework #1

Homework #1

Due: 11:58pm on Monday, April 7, 2014

You will receive no credit for items you complete after the assignment is due. Grading Policy

Video Solution Problem for Chapter 12 Sections 1-2 - Particle Kinematics.

Watch the following video and answer the question.

Part A

A particle is moving along a straight line through a fluid medium such that its speed is measured as v = (2t)~m/s, where

\texttip{t}{t} is in seconds. If it is released from rest at s = 0, determine its positions and acceleration when t = 3~s.

ANSWER:

Correct

Problem 12.4

\rm s = 9~m,~a = 2~m/s^2

\rm s = 2~m,~a = 9~m/s^2

\rm s = 2~m,~a = 18~m/s^2

\rm s = 18~m,~a = 2~m/s^2

Traveling with an initial speed of 40{\rm \; km/h} , a car accelerates at 6000{\rm \; km/h^2} along a straight road.

Part A

How long will it take to reach a speed of 120{\rm \; km/h} ?

Express your answer using three significant figures and include the appropriate units.

ANSWER:

Correct

Part B

Through what distance does the car travel during this time?


ANSWER:

Correct

Problem 12.7

A bicyclist starts from rest and after traveling along a straight path a distance of 35 {\rm m} reaches a speed of 32 {\rm

km}/{\rm h}.

Part A

Determine his acceleration if it is constant.


ANSWER:

Correct

Part B

Also, how long does it take to reach the speed of 32 {\rm km}/{\rm h}?


ANSWER:

t = 48.0 {\rm s}

s = 1070 {\rm m}

a = 1.13 \large{{\rm \frac{m}{s {̂2}}}}

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Correct

Problem 12.29

A particle moves along a straight line with an acceleration a=2v {̂1/2}\; {\rm m/s^2}, where v is in {\rm m/s}.

Part A

If s = 0, v = 9 {\rm m/s} when t = 0, determine the time for the particle to achieve a velocity of 23 {\rm m/s}.


ANSWER:

Correct

Part B

Also, find the displacement of particle when t = 6 {\rm s}.


ANSWER:

All attempts used; correct answer displayed

Problem 12.32

The acceleration of a particle traveling along a straight line is \large{a=\frac{1}{6}s^{1/2} \; {\rm m/s^2}}, where { s} is in

meters.

Part A

If v = 0, s = 4 {\rm m} when t = 0, determine the particle's velocity at s = 7 {\rm m}.

Express your answer using three significant figures and include the appropriate units

ANSWER:

t = 7.88 {\rm s}

t = 1.80 {\rm s}

s = 234 {\rm m}

v = 1.53 \large{{\rm \frac{m}{s}}}

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Correct

Video Solution Problem for Chapter 12 Section 3 - Rectilinear Kinematics of a Particle.


Part A

A car travels up a hill with the speed shown in the graph. Compute the total distance the car moves until it stops at

\rm t = 60~s. What is the acceleration at \rm t = 45~s?

ANSWER:

Processing math: 0%

Correct

Problem 12.69

The v-s graph for the car is given for the first 500 {\rm ft} of its motion.

Part A

Construct the a-s graph for 0 \le s \le 500 \;{\rm{ ft}}.

ANSWER:

\rm s = 400~m,~a_{45} = -3.00~m/s^2

\rm s = 450~m,~a_{45} = -0.333~m/s^2

\rm s = 450~m,~a_{45} = 0.333~m/s^2

\rm s = 400~m,~a_{45} = -3.00~m/s^2

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Correct

Part B

How long does it take to travel the 500-{\rm ft} distance? The car starts at s = 0 when t = 0.


ANSWER:

Correct

Video Solution Problem for Chapter 12 Sections 4-6 - Projectile Motion of a Particle.


t = 17.9 {\rm s}

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Part A

The motorcyclist attempts to jump over a series of cars and trucks and lands smoothly on the other ramp, i.e., such

that his velocity is tangent to the ramp at \texttip{B}{B}. Determine the launch speed \rm v_A necessary to make the

jump.

ANSWER:

Correct

\rm v_A = 11.07~m/s

\rm v_A = 11.90~m/s

\rm v_A = 15.66~m/s

\rm v_A = 16.83~m/s

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± Speed of a Softball

Learning Goal:

To be able to calculate the velocity and the angle of trajectory of an object undergoing projectile motion.

A batter hits a softball over a third baseman's head with speed

\texttip{v_{\rm 0}}{v_0} and at an angle \texttip{\theta }{theta} from

the horizontal. Immediately after the ball is hit, the third baseman

turns and runs at a constant velocity v = 7.000 \;{\rm m/s}, for a

time t =2.000 \;{\rm s}. He then catches the ball at the same

height at which it left the bat. The third baseman was initially l

=18.00 \; {\rm m} from home plate (the location where the ball

was hit from).

Part A - Initial velocity of the softball

Find \texttip{v_{\rm 0}}{v_0}. Use g=9.807 \;{\rm m}/{\rm s}^2 for the magnitude of the acceleration due to gravity.

Assume that there is no air resistance.

Express the initial speed to four significant figures in meters per second.

Hint 1. How to approach the problem

To find the initial velocity \texttip{v_{\rm 0}}{v_0}, calculate the horizontal, \texttip{v_{0x}}{v_{0x}}, and vertical,

\texttip{v_{0y}}{v_{0y}}, components of the initial velocity. You can find the initial velocity using the following

relationship:

v_0 = \sqrt {v^2_{0x} + v^2_{0y}}

Hint 2. Find the initial velocity of the softball in the x direction

Because we have assumed that there is no air resistance, the horizontal component of the ball's velocity is

constant and can be found from the distance covered by the ball and the time in which such distance is covered.

What is v_{0x}?

Express your answer in terms of \texttip{l}{l}, \texttip{v}{v}, and \texttip{t}{t}.

Hint 1. Determine the distance traveled in the x direction

After being hit, the ball reaches the third baseman’s original location and moves beyond it. What is the

distance \texttip{x}{x} the ball travels horizontally before it is caught?

Express your answer in terms of \texttip{l}{l}, \texttip{v}{v}, and \texttip{t}{t}.

ANSWER:Processing math: 0%

ANSWER:

Hint 3. Find the initial velocity of the softball in the y direction

Using the kinematic equation in the y direction,

\large{y(t)=y_0+v_{y0}t-\frac{gt^2}{2}}

find an expression for v_{0y}. Recall that the ball’s final height equals the ball’s initial height.

Express your answer in terms of \texttip{g}{g} and \texttip{t}{t}.

ANSWER:

ANSWER:

Correct

Part B - Angle of trajectory

Find the angle \texttip{\theta }{theta} in degrees.

Express your answer numerically to four significant figures in degrees.

ANSWER:

Correct

Part C - Velocity of the softball

Find the components \texttip{v_{\mit x}}{v_x} and \texttip{v_{\mit y}}{v_y} of the ball’s velocity, \texttip{{\bf v}}{v_evec},

0.100 \rm s before the ball is caught.

Express your answers for \texttip{v_{\mit x}}{v_x} and \texttip{v_{\mit y}}{v_y} numerically to three significant

figures in meters per second, separated by a comma.

\texttip{x}{x} = l+v t

v_{0x} = \large{\frac{l+v t}{t}}

v_{0y} = \large{\frac{1}{2} g t}

v_{0} = 18.77 \rm m/s

\texttip{\theta }{theta} = 31.51 \rm degrees

Processing math: 0%

You did not open hints for this part.

ANSWER:

Part D - The position of the softball before the ball is caught

Find the vector components x and y of the ball’s position, \texttip{{\bf r}}{r_evec}, 0.100 \rm s before the ball is caught.

Express your answers for x and y numerically to three significant figures in meters, separated by a comma.

You did not open hints for this part.

ANSWER:

Problem 12.82

A rocket is fired from rest at x = 0 and travels along a parabolic trajectory described by y^2=[190(10^3)x] \;{\rm m}.

Part A

If the x component of acceleration is \large{a_x=\left( \frac{1}{3}t^2 \right) \; {\rm m/s^2}}, where t is in seconds,

determine the magnitude of the rocket's velocity when t = 8 {\rm s}.


ANSWER:

Correct

Part B

Determine the magnitude of the rocket's acceleration when t = 8 {\rm s}.


ANSWER:

\texttip{{\bf v}}{v_evec} = \rm m/s

\texttip{{\bf r}}{r_evec} = \rm m

v = 1160 \large{{\rm \frac{m}{s}}}

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Correct

Problem 12.86

When a rocket reaches an altitude of 40 {\rm m} it begins to travel along the parabolic path \left( {y\; - \;40} \right)^2 =

160x, where the coordinates are measured in meters.

Part A

If the component of velocity in the vertical direction is constant at v_y = 200 {\rm{ m}}/{\rm{s}}, determine the

magnitude of the rocket's velocity when it reaches an altitude of 160 {\rm m}.


ANSWER:

Correct

Part B

Determine the magnitude of the rocket's acceleration when it reaches an altitude of 160 {\rm m}.


ANSWER:

a = 147 \large{{\rm \frac{m}{s {̂2}}}}

v = 361 \large{{\rm \frac{m}{s}}}

a = 500 \large{{\rm \frac{m}{s {̂2}}}}

Processing math: 0%

Correct

Problem 12.94

From a videotape, it was observed that a player kicked a football 126 {\rm ft} during a measured time of 2.9 seconds.

Part A

Determine the initial speed of the ball.


ANSWER:

Correct

Part B

Determine the angle \theta at which it was kicked.


ANSWER:

Correct

Problem 12.103

The ball is thrown from the tower with a velocity of 20 {\rm ft}/{\rm s} as shown.

v_0 = 63.8 \large{{\rm \frac{ft}{s}}}

\theta = 47.1 {\rm \degree}

Processing math: 0%

Part A

Determine the x and y coordinates to where the ball strikes the slope.

Enter the x and y coordinates using three significant figures separated by a comma.

ANSWER:

Correct

Part B

Also, determine the speed at which the ball hits the ground.


ANSWER:

Correct

Problem 12.112

The baseball player A hits the baseball at v_A = 41{\rm ft/s} and \theta _A = 57{\rm \degree} from the horizontal. When the

ball is directly overhead of player B he begins to run under it.

Part A

Determine the constant speed at which B must run in order to make the catch at the same elevation at which the ball

was hit.

Express your answer to three significant figures and

x, y = 32.3,6.17 \rm ft

v = 71.8 \large{{\rm \frac{ft}{s}}}

Processing math: 0%

include the appropriate units.

ANSWER:

Correct

Part B

Determine the distance d in order to make the catch at the same elevation at which the ball was hit.

Express your answer to three significant figures and include the appropriate units.

ANSWER:

Correct

Score Summary:

Your score on this assignment is 92.9%.

You received 92.9 out of a possible total of 100 points.

v_B = 22.3 \large{{\rm \frac{ft}{s}}}

d = 32.7 {\rm ft}

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