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  1. Preface
  2. Unit 1. Mechanics
    1. 1 Units and Measurement
      1. Introduction
      2. 1.1 The Scope and Scale of Physics
      3. 1.2 Units and Standards
      4. 1.3 Unit Conversion
      5. 1.4 Dimensional Analysis
      6. 1.5 Estimates and Fermi Calculations
      7. 1.6 Significant Figures
      8. 1.7 Solving Problems in Physics
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 2 Vectors
      1. Introduction
      2. 2.1 Scalars and Vectors
      3. 2.2 Coordinate Systems and Components of a Vector
      4. 2.3 Algebra of Vectors
      5. 2.4 Products of Vectors
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 3 Motion Along a Straight Line
      1. Introduction
      2. 3.1 Position, Displacement, and Average Velocity
      3. 3.2 Instantaneous Velocity and Speed
      4. 3.3 Average and Instantaneous Acceleration
      5. 3.4 Motion with Constant Acceleration
      6. 3.5 Free Fall
      7. 3.6 Finding Velocity and Displacement from Acceleration
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 4 Motion in Two and Three Dimensions
      1. Introduction
      2. 4.1 Displacement and Velocity Vectors
      3. 4.2 Acceleration Vector
      4. 4.3 Projectile Motion
      5. 4.4 Uniform Circular Motion
      6. 4.5 Relative Motion in One and Two Dimensions
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    5. 5 Newton's Laws of Motion
      1. Introduction
      2. 5.1 Forces
      3. 5.2 Newton's First Law
      4. 5.3 Newton's Second Law
      5. 5.4 Mass and Weight
      6. 5.5 Newton’s Third Law
      7. 5.6 Common Forces
      8. 5.7 Drawing Free-Body Diagrams
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    6. 6 Applications of Newton's Laws
      1. Introduction
      2. 6.1 Solving Problems with Newton’s Laws
      3. 6.2 Friction
      4. 6.3 Centripetal Force
      5. 6.4 Drag Force and Terminal Speed
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    7. 7 Work and Kinetic Energy
      1. Introduction
      2. 7.1 Work
      3. 7.2 Kinetic Energy
      4. 7.3 Work-Energy Theorem
      5. 7.4 Power
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    8. 8 Potential Energy and Conservation of Energy
      1. Introduction
      2. 8.1 Potential Energy of a System
      3. 8.2 Conservative and Non-Conservative Forces
      4. 8.3 Conservation of Energy
      5. 8.4 Potential Energy Diagrams and Stability
      6. 8.5 Sources of Energy
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    9. 9 Linear Momentum and Collisions
      1. Introduction
      2. 9.1 Linear Momentum
      3. 9.2 Impulse and Collisions
      4. 9.3 Conservation of Linear Momentum
      5. 9.4 Types of Collisions
      6. 9.5 Collisions in Multiple Dimensions
      7. 9.6 Center of Mass
      8. 9.7 Rocket Propulsion
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    10. 10 Fixed-Axis Rotation
      1. Introduction
      2. 10.1 Rotational Variables
      3. 10.2 Rotation with Constant Angular Acceleration
      4. 10.3 Relating Angular and Translational Quantities
      5. 10.4 Moment of Inertia and Rotational Kinetic Energy
      6. 10.5 Calculating Moments of Inertia
      7. 10.6 Torque
      8. 10.7 Newton’s Second Law for Rotation
      9. 10.8 Work and Power for Rotational Motion
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    11. 11 Angular Momentum
      1. Introduction
      2. 11.1 Rolling Motion
      3. 11.2 Angular Momentum
      4. 11.3 Conservation of Angular Momentum
      5. 11.4 Precession of a Gyroscope
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    12. 12 Static Equilibrium and Elasticity
      1. Introduction
      2. 12.1 Conditions for Static Equilibrium
      3. 12.2 Examples of Static Equilibrium
      4. 12.3 Stress, Strain, and Elastic Modulus
      5. 12.4 Elasticity and Plasticity
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    13. 13 Gravitation
      1. Introduction
      2. 13.1 Newton's Law of Universal Gravitation
      3. 13.2 Gravitation Near Earth's Surface
      4. 13.3 Gravitational Potential Energy and Total Energy
      5. 13.4 Satellite Orbits and Energy
      6. 13.5 Kepler's Laws of Planetary Motion
      7. 13.6 Tidal Forces
      8. 13.7 Einstein's Theory of Gravity
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    14. 14 Fluid Mechanics
      1. Introduction
      2. 14.1 Fluids, Density, and Pressure
      3. 14.2 Measuring Pressure
      4. 14.3 Pascal's Principle and Hydraulics
      5. 14.4 Archimedes’ Principle and Buoyancy
      6. 14.5 Fluid Dynamics
      7. 14.6 Bernoulli’s Equation
      8. 14.7 Viscosity and Turbulence
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  3. Unit 2. Waves and Acoustics
    1. 15 Oscillations
      1. Introduction
      2. 15.1 Simple Harmonic Motion
      3. 15.2 Energy in Simple Harmonic Motion
      4. 15.3 Comparing Simple Harmonic Motion and Circular Motion
      5. 15.4 Pendulums
      6. 15.5 Damped Oscillations
      7. 15.6 Forced Oscillations
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 16 Waves
      1. Introduction
      2. 16.1 Traveling Waves
      3. 16.2 Mathematics of Waves
      4. 16.3 Wave Speed on a Stretched String
      5. 16.4 Energy and Power of a Wave
      6. 16.5 Interference of Waves
      7. 16.6 Standing Waves and Resonance
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 17 Sound
      1. Introduction
      2. 17.1 Sound Waves
      3. 17.2 Speed of Sound
      4. 17.3 Sound Intensity
      5. 17.4 Normal Modes of a Standing Sound Wave
      6. 17.5 Sources of Musical Sound
      7. 17.6 Beats
      8. 17.7 The Doppler Effect
      9. 17.8 Shock Waves
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  4. A | Units
  5. B | Conversion Factors
  6. C | Fundamental Constants
  7. D | Astronomical Data
  8. E | Mathematical Formulas
  9. F | Chemistry
  10. G | The Greek Alphabet
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
    14. Chapter 14
    15. Chapter 15
    16. Chapter 16
    17. Chapter 17
  12. Index

Check Your Understanding

4.1

(a) Taking the derivative with respect to time of the position function, we have v(t)=9.0t2i^andv(3.0s)=81.0i^m/s.v(t)=9.0t2i^andv(3.0s)=81.0i^m/s. (b) Since the velocity function is nonlinear, we suspect the average velocity is not equal to the instantaneous velocity. We check this and find
vavg=r(t2)r(t1)t2t1=r(4.0s)r(2.0s)4.0s2.0s=(144.0i^36.0i^)m2.0s=54.0i^m/s,vavg=r(t2)r(t1)t2t1=r(4.0s)r(2.0s)4.0s2.0s=(144.0i^36.0i^)m2.0s=54.0i^m/s,
which is different from v(3.0s)=81.0i^m/s.v(3.0s)=81.0i^m/s.

4.2

The acceleration vector is constant and doesn’t change with time. If a, b, and c are not zero, then the velocity function must be linear in time. We have v(t)=adt=(ai^+bj^+ck^)dt=(ai^+bj^+ck^)tm/s,v(t)=adt=(ai^+bj^+ck^)dt=(ai^+bj^+ck^)tm/s, since taking the derivative of the velocity function produces a(t).a(t). If any of the components of the acceleration are zero, then that component of the velocity would be a constant.

4.3

(a) Choose the top of the cliff where the rock is thrown from the origin of the coordinate system. Although it is arbitrary, we typically choose time t = 0 to correspond to the origin. (b) The equation that describes the horizontal motion is x=x0+vxt.x=x0+vxt. With x0=0,x0=0, this equation becomes x=vxt.x=vxt. (c) Equation 4.16 through Equation 4.18 and Equation 4.19 describe the vertical motion, but since y0=0andv0y=0,y0=0andv0y=0, these equations simplify greatly to become y=12(v0y+vy)t=12vyt,y=12(v0y+vy)t=12vyt,vy=gt,vy=gt,y=12gt2,y=12gt2, and vy2=−2gy.vy2=−2gy. (d) We use the kinematic equations to find the x and y components of the velocity at the point of impact. Using vy2=−2gyvy2=−2gy and noting the point of impact is −100.0 m, we find the y component of the velocity at impact is vy=44.3m/s.vy=44.3m/s. We are given the x component, vx=15.0m/s,vx=15.0m/s, so we can calculate the total velocity at impact: v = 46.8 m/s and θ=71.3°θ=71.3° below the horizontal.

4.4

The golf shot at 30°.30°.

4.5

134.0 cm/s

4.6

Labeling subscripts for the vector equation, we have B = boat, R = river, and E = Earth. The vector equation becomes vBE=vBR+vRE.vBE=vBR+vRE. We have right triangle geometry shown in Figure 04_05_BoatRiv_img. Solving for vBEvBE, we have
vBE=vBR2+vRE2=4.52+3.02vBE=vBR2+vRE2=4.52+3.02
vBE=5.4m/s,θ=tan−1(3.04.5)=33.7°.vBE=5.4m/s,θ=tan−1(3.04.5)=33.7°.

Vectors V sub B W, V sub W E and V sub B E form a right triangle. A boat is shown at the vertex where the tails of V sub B W and V sub B E meet. Vector V sub B W points up. V sub W E points to the right. V sub B E points up and right, at an angle to the vertical. V sub B E is the vector sum of v sub B W and V sub W E.

Conceptual Questions

1.

straight line

3.

The slope must be zero because the velocity vector is tangent to the graph of the position function.

5.

No, motions in perpendicular directions are independent.

7.

a. no; b. minimum at apex of trajectory and maximum at launch and impact; c. no, velocity is a vector; d. yes, where it lands

9.

They both hit the ground at the same time.

11.

yes

13.

If he is going to pass the ball to another player, he needs to keep his eyes on the reference frame in which the other players on the team are located.

15.
Figure a: a hat’s trajectory is straight down. Figure b: a hat’s trajectory is parabolic, curving down and to the left.

Problems

17.

r=1.0i^4.0j^+6.0k^r=1.0i^4.0j^+6.0k^

19.

ΔrTotal=472.0mi^+80.3mj^ΔrTotal=472.0mi^+80.3mj^

21.

Sum of displacements=−6.4kmi^+9.4kmj^Sum of displacements=−6.4kmi^+9.4kmj^

23.

a. v(t)=8.0ti^+6.0t2k^,v(0)=0,v(1.0)=8.0i^+6.0k^m/sv(t)=8.0ti^+6.0t2k^,v(0)=0,v(1.0)=8.0i^+6.0k^m/s,
b. vavg=4.0i^+2.0k^m/svavg=4.0i^+2.0k^m/s

25.

Δr1=20.00mj^,Δr2=(2.000×104m)(cos30°i^+sin30°j^)Δr1=20.00mj^,Δr2=(2.000×104m)(cos30°i^+sin30°j^)
Δr=1.700×104mi^+1.002×104mj^Δr=1.700×104mi^+1.002×104mj^

27.

a. v(t)=(4.0ti^+3.0tj^)m/s,v(t)=(4.0ti^+3.0tj^)m/s,r(t)=(2.0t2i^+32t2j^)mr(t)=(2.0t2i^+32t2j^)m,
b. x(t)=2.0t2m,y(t)=32t2m,t2=x2y=34xx(t)=2.0t2m,y(t)=32t2m,t2=x2y=34x

A graph of the linear function y equals 3 quarters x. The graph is a straight, positive slope line through the origin.
29.

a. v(t)=(6.0ti^21.0t2j^+10.0t−3k^)m/sv(t)=(6.0ti^21.0t2j^+10.0t−3k^)m/s,
b. a(t)=(6.0i^42.0tj^30t−4k^)m/s2a(t)=(6.0i^42.0tj^30t−4k^)m/s2,
c. v(2.0s)=(12.0i^84.0j^+1.25k^)m/sv(2.0s)=(12.0i^84.0j^+1.25k^)m/s,
d. v(1.0s)=6.0i^21.0j^+10.0k^m/s,|v(1.0s)|=24.0m/sv(1.0s)=6.0i^21.0j^+10.0k^m/s,|v(1.0s)|=24.0m/s
v(3.0s)=18.0i^189.0j^+0.37k^m/s,v(3.0s)=18.0i^189.0j^+0.37k^m/s,|v(3.0s)|=190.0m/s|v(3.0s)|=190.0m/s,
e. r(t)=(3.0t2i^7.0t3j^5.0t−2k^)mr(t)=(3.0t2i^7.0t3j^5.0t−2k^)m
vavg=9.0i^49.0j^+3.75k^m/svavg=9.0i^49.0j^+3.75k^m/s

31.

a. v(t)=−sin(1.0t)i^+cos(1.0t)j^+k^v(t)=−sin(1.0t)i^+cos(1.0t)j^+k^, b. a(t)=−cos(1.0t)i^sin(1.0t)j^a(t)=−cos(1.0t)i^sin(1.0t)j^

33.

a. t=0.55st=0.55s, b. x=110mx=110m

35.

a. t=0.24s,d=0.28mt=0.24s,d=0.28m, b. They aim high.

An illustration of a person throwing a dart. The dart is released horizontally a distance of 2.4 meters from the dart board, level with the bulls eye of the dart board, with a speed of 10 meters per second.
37.

a., t=12.8s,x=5619mt=12.8s,x=5619m b. vy=125.0m/s,vx=439.0m/s,|v|=456.0m/svy=125.0m/s,vx=439.0m/s,|v|=456.0m/s

39.

a. vy=v0ygt,t=10s,vy=0,v0y=98.0m/s,v0=196.0m/svy=v0ygt,t=10s,vy=0,v0y=98.0m/s,v0=196.0m/s, b. h=490.0m,h=490.0m,
c. v0x=169.7m/s,x=3394.0m,v0x=169.7m/s,x=3394.0m,
d. x=169.7m/s(15.0s)=2545.5m y=(98.0m/s)(15.0s)2=367.5m s=2545.5mi^+367.5mj^x=169.7m/s(15.0s)=2545.5m y=(98.0m/s)(15.0s)2=367.5m s=2545.5mi^+367.5mj^

41.

−100m=(−2.0m/s)t(4.9m/s2)t2,−100m=(−2.0m/s)t(4.9m/s2)t2, t=4.3s,t=4.3s,x=86.0mx=86.0m

43.

RMoon=48mRMoon=48m

45.

a. v0y=24m/sv0y=24m/svy2=v0y22gyh=29.3mvy2=v0y22gyh=29.3m,
b. t=2.4sv0x=18m/sx=43.2mt=2.4sv0x=18m/sx=43.2m,
c. y=−100my0=0y=−100my0=0 yy0=v0yt12gt2100=24t4.9t2yy0=v0yt12gt2100=24t4.9t2 t=7.58st=7.58s,
d. x=136.44mx=136.44m,
e. t=2.0sy=28.4mx=36mt=2.0sy=28.4mx=36m
t=4.0sy=17.6mx=72mt=4.0sy=17.6mx=72m
t=6.0sy=−32.4mx=108mt=6.0sy=−32.4mx=108m

47.

v0y=12.9m/syy0=v0yt12gt220.0=12.9t4.9t2v0y=12.9m/syy0=v0yt12gt220.0=12.9t4.9t2
t=3.7sv0x=15.3m/sx=56.7mt=3.7sv0x=15.3m/sx=56.7m
So the golfer’s shot lands 13.3 m short of the green.

49.

a. R=60.8mR=60.8m,
b. R=137.8mR=137.8m

51.

a. vy2=v0y22gyy=2.9m/svy2=v0y22gyy=2.9m/s
y=3.3m/sy=3.3m/s
y=v0y22g=(v0sinθ)22gsinθ=0.91θ=65.5°y=v0y22g=(v0sinθ)22gsinθ=0.91θ=65.5°

53.

R=18.5mR=18.5m

55.

y=(tanθ0)x[g2(v0cosθ0)2]x2v0=16.4m/sy=(tanθ0)x[g2(v0cosθ0)2]x2v0=16.4m/s

57.

R=v02sin2θ0gθ0=15.9°R=v02sin2θ0gθ0=15.9°

59.

It takes the wide receiver 1.1 s to cover the last 10 m of his run.
Ttof=2(v0sinθ)gsinθ=0.27θ=15.6°Ttof=2(v0sinθ)gsinθ=0.27θ=15.6°

61.

aC=40m/s2aC=40m/s2

63.

aC=v2rv2=raC=78.4,v=8.85m/saC=v2rv2=raC=78.4,v=8.85m/s
T=5.68s,T=5.68s, which is 0.176rev/s=10.6rev/min0.176rev/s=10.6rev/min

65.

Venus is 108.2 million km from the Sun and has an orbital period of 0.6152 y.
r=1.082×1011mT=1.94×107sr=1.082×1011mT=1.94×107s
v=3.5×104m/s,aC=1.135×10−2m/s2v=3.5×104m/s,aC=1.135×10−2m/s2

67.

360rev/min=6rev/s360rev/min=6rev/s
v=3.8m/sv=3.8m/s aC=144.m/s2aC=144.m/s2

69.

a. O(t)=(4.0i^+3.0j^+5.0k^)tmO(t)=(4.0i^+3.0j^+5.0k^)tm,
b. rPS=rPS+rSS,rPS=rPS+rSS, r(t)=r(t)+(4.0i^+3.0j^+5.0k^)tmr(t)=r(t)+(4.0i^+3.0j^+5.0k^)tm,
c. v(t)=v(t)+(4.0i^+3.0j^+5.0k^)m/sv(t)=v(t)+(4.0i^+3.0j^+5.0k^)m/s, d. The accelerations are the same.

71.

vPC=(2.0i^+5.0j^+4.0k^)m/svPC=(2.0i^+5.0j^+4.0k^)m/s

73.

a. A = air, S = seagull, G = ground
vSA=9.0m/svSA=9.0m/s velocity of seagull with respect to still air
vAG=?vSG=5m/svAG=?vSG=5m/s vSG=vSA+vAGvAG=vSGvSAvSG=vSA+vAGvAG=vSGvSA
vAG=−4.0m/svAG=−4.0m/s
b. vSG=vSA+vAGvSG=−13.0m/svSG=vSA+vAGvSG=−13.0m/s
−6000m−13.0m/s=7 min 42 s−6000m−13.0m/s=7 min 42 s

75.

Take the positive direction to be the same direction that the river is flowing, which is east. S = shore/Earth, W = water, and B = boat.
a. vBS=11km/hvBS=11km/h
t=8.2mint=8.2min
b. vBS=−5km/hvBS=−5km/h
t=18mint=18min
c. vBS=vBW+vWSvBS=vBW+vWS θ=22°θ=22° west of north

Vectors V sub B W, V sub W S and V sub B S form a right triangle, with V sub B W as the hypotenuse. V sub B S points up. V sub W S points to the right. V sub B W points up and left, at an angle of theta to the vertical. V sub B S is the vector sum of v sub B W and V sub W S.


d. |vBS|=7.4km/h|vBS|=7.4km/h t=6.5mint=6.5min
e. vBS=8.54km/h,vBS=8.54km/h, but only the component of the velocity straight across the river is used to get the time

Vectors V sub B W, V sub W S and V sub B S form a right triangle, with V sub B S as the hypotenuse. V sub B W points up. V sub W S points to the right. V sub B S points up and right, at an angle of theta to the vertical. V sub B S is the vector sum of v sub B W and V sub W S.


t=6.0mint=6.0min
Downstream = 0.3 km

77.

vAG=vAC+vCGvAG=vAC+vCG
|vAC|=25km/h|vCG|=15km/h|vAG|=29.15km/h|vAC|=25km/h|vCG|=15km/h|vAG|=29.15km/h vAG=vAC+vCGvAG=vAC+vCG
The angle between vACvAC and vAGvAG is 31°,31°, so the direction of the wind is 14°14° north of east.

Vectors V sub A C, V sub C G and V sub A G form a triangle. V sub A C and V sub C G are at right angles. V sub A G is the vector sum of v sub A C and V sub C G.

Additional Problems

79.

aC=39.6m/s2aC=39.6m/s2

81.

90.0km/h=25.0m/s,9.0km/h=2.5m/s,90.0km/h=25.0m/s,9.0km/h=2.5m/s, 60.0km/h=16.7m/s60.0km/h=16.7m/s
aT=−2.5m/s2,aC=1.86m/s2,a=3.1m/s2aT=−2.5m/s2,aC=1.86m/s2,a=3.1m/s2

83.

The radius of the circle of revolution at latitude λλ is REcosλ.REcosλ. The velocity of the body is 2πrT.aC=4π2REcosλT22πrT.aC=4π2REcosλT2 for λ=40°,aC=0.26%gλ=40°,aC=0.26%g

85.

aT=3.00m/s2aT=3.00m/s2
v(5s)=15.00m/saC=150.00m/s2θ=88.8°v(5s)=15.00m/saC=150.00m/s2θ=88.8° with respect to the tangent to the circle of revolution directed inward. |a|=150.03m/s2|a|=150.03m/s2

87.

a(t)=Aω2cosωti^Aω2sinωtj^a(t)=Aω2cosωti^Aω2sinωtj^
aC=5.0mω2ω=0.89rad/saC=5.0mω2ω=0.89rad/s
v(t)=−2.24m/si^3.87m/sj^v(t)=−2.24m/si^3.87m/sj^

89.

r1=1.5j^+4.0k^r2=Δr+r1=2.5i^+4.7j^+2.8k^r1=1.5j^+4.0k^r2=Δr+r1=2.5i^+4.7j^+2.8k^

91.

vx(t)=265.0m/svx(t)=265.0m/s
vy(t)=20.0m/svy(t)=20.0m/s
v(5.0s)=(265.0i^+20.0j^)m/sv(5.0s)=(265.0i^+20.0j^)m/s

93.

R=1.07mR=1.07m

95.

v0=20.1m/sv0=20.1m/s

97.

v=3072.5m/sv=3072.5m/s
aC=0.223m/s2aC=0.223m/s2

Challenge Problems

99.

a. 400.0m=v0yt4.9t2359.0m=v0xtt=359.0v0x400.0=359.0v0yv0x4.9(359.0v0x)2400.0m=v0yt4.9t2359.0m=v0xtt=359.0v0x400.0=359.0v0yv0x4.9(359.0v0x)2
−400.0=359.0tan40631,516.9v0x2v0x2=900.6v0x=30.0m/sv0y=v0xtan40=25.2m/s−400.0=359.0tan40631,516.9v0x2v0x2=900.6v0x=30.0m/sv0y=v0xtan40=25.2m/s
v=39.2m/sv=39.2m/s, b. t=12.0st=12.0s

101.

a. rTC=(−32+80t)i^+50tj^,|rTC|2=(−32+80t)2+(50t)2rTC=(−32+80t)i^+50tj^,|rTC|2=(−32+80t)2+(50t)2
2rdrdt=2(−32+80t)(80)+5000tdrdt=160(−32+80t)+5000t2r=02rdrdt=2(−32+80t)(80)+5000tdrdt=160(−32+80t)+5000t2r=0
17800t=5184t=0.29 hr17800t=5184t=0.29 hr,
b. |rTC|=17km|rTC|=17km

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