A ball thrown horizontally at 20 m/s travels a horizontal distance of 40 m before hitting the ground. From what height was the ball thrown?
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Table of Contents
1
Concepts of Motion
1.1
Motion Diagrams
1.2
Models and Modeling
1.3
Position, Time, and Displacement
1.4
Velocity
1.5
Linear Acceleration
1.6
Motion in One Dimension
1.7
Solving Problems in Physics
1.8
Units and Significant Figures
2
Kinematics in One Dimension
2.1
Uniform in Motion
2.2
Instantaneous Velocity
2.3
Finding Position from Velocity
2.4
Motion with Constant Acceleration
2.5
Free Fall
2.6
Motion on an Inclined Plane
2.7
Instantaneous Acceleration
3
Vectors and Coordinate Systems
3.1
Scalars and Vectors
3.2
Using Vectors
3.3
Coordinate Systems and Vector Components
3.4
Unit Vectors and Vector Algebra
4
Kinematics in Two Dimensions
4.1
Motion in Two Dimensions
4.2
Projectile Motion
4.3
Relative Motion
4.4
Uniform Circular Motion
4.5
Centripetal Acceleration
4.6
Nonuniform Circular Motion
5
Force and Motion
5.3
Identifying Forces
5.4
What Do Forces Do?
5.5
Newton's Second Law
5.6
Newton's First Law
5.7
Free-Body Diagrams
6
Dynamics I: Motion Along a Line
6.1
The Equilibrium Model
6.2
Using Newton's Second Law
6.3
Mass, Weight, and Gravity
6.4
Friction
6.5
Drag
7
Newton’s Third Law
7.2
Analyzing Interacting Objects
7.3
Newton's Third Law
7.4
Ropes and Pulleys
8
Dynamics II: Motion in a Plane
8.1
Dynamics in Two Dimensions
8.2
Uniform Circular Motion
8.3
Circular Orbits
8.4
Reasoning About Circular Motion
8.5
Nonuniform Circular Motion
9
Work and Kinetic Energy
9.2
Work and Kinetic Energy for a Single Particle
9.3
Calculating the Work Done
9.4
Restoring Forces and the Work Done by a Spring
9.5
Dissipative Forces and Thermal Energy
9.6
Power
10
Interactions and Potential Energy
10.1
Potential Energy
10.2
Gravitational Potential Energy
10.3
Elastic Potential Energy
10.4
Conservation of Energy
10.5
Energy Diagrams
10.6
Force and Potential Energy
10.7
Conservative and Nonconservative Forces
10.8
The Energy Principle Revisited
11
Impulse and Momentum
11.1
Momentum and Impulse
11.2
Conservation of Momentum
11.3
Collisions
11.4
Explosions
11.5
Momentum in Two Dimensions
11.6
Rocket Propulsion
12
Rotation of a Rigid Body
12.1
Rotational Motion
12.10
The Vector Description of Rotational Motion
12.11
Angular Momentum
12.12
Precession of a Gyroscope
12.2
Rotation About the Center of Mass
12.3
Rotational Energy
12.4
Calculating Moment of Inertia
12.5
Torque
12.6
Rotational Dynamics
12.7
Rotation About a Fixed Axis
12.8
Static Equilibrium
12.9
Rolling Motion
13
Newton’s Theory of Gravity
13.3
Newton’s Law of Gravity
13.4
Little g and Big G
13.5
Gravitational Potential Energy
13.6
Satellite Orbits and Energies
14
Fluids and Elasticity
14.1
Fluids
14.2
Pressure
14.3
Measuring and Using Pressure
14.4
Buoyancy
14.5
Fluid Dynamics
14.6
Motion of a Viscous Fluid
14.7
Elasticity
15
Oscillations
15.1
Simple Harmonic Motion
15.2
SHM and Circular Motion
15.3
Energy in SHM
15.4
The Dynamics of SHM
15.5
Vertical Oscillations
15.6
The Pendulum
15.7
Damped Oscillations
15.8
Driven Oscillations and Resonance
15.9
Coupled Oscillations and Normal Modes
16
Traveling Waves
16.1
An Introduction to Waves
16.2
One-Dimensional Waves
16.3
Sinusoidal Waves
16.4
The Wave Equation on a String
16.5
Sound and Light
16.6
The Wave Equation in a Fluid
16.7
Waves in Two and Three Dimensions
16.8
Power, Intensity, and Decibels
16.9
The Doppler Effect
17
Superposition
17.1
The Principle of Superposition
17.2
Standing Waves
17.3
Standing Waves on a String
17.4
Standing Sound Waves and Musical Acoustics
17.5
Interference in One Dimension
17.6
The Mathematics of Interference
17.7
Interference in Two and Three Dimensions
17.8
Beats
18
A Macroscopic Description of Matter
18.1
Solids, Liquids, and Gases
18.2
Atoms and Moles
18.3
Temperature
18.4
Thermal Expansion
18.5
Phase Changes
18.6
Ideal Gases
18.7
Ideal-Gas Processes
19
Work, Heat, and the First Law of Thermodynamics
19.1
It’s All About Energy
19.2
Work in Ideal-Gas Processes
19.3
Heat
19.4
The First Law of Thermodynamics
19.5
Thermal Properties of Matter
19.6
Calorimetry
19.7
The Specific Heats of Gases
19.8
Heat-Transfer Mechanisms
20
The Micro/Macro Connection
20.1
Connecting the Microscopic and the Macroscopic
20.2
Molecular Speeds and Collisions
20.3
Pressure in a Gas
20.4
Temperature
20.5
Thermal Energy and Specific Heat
20.6
Heat Transfer and Thermal Equilibrium
20.7
Irreversible Processes and the Second Law of Thermodynamics
20.8
Microstates, Multiplicity, and Entropy
20.9
Using Entropy
21
Heat Engines and Refrigerators
21.1
Turning Heat into Work
21.2
Heat Engines and Refrigerators
21.3
Ideal-Gas Heat Engines
21.4
Ideal-Gas Refrigerators
21.5
The Limits of Efficiency
21.6
The Carnot Cycle
22
Electric Charges and Forces
22.1
The Charge Model
22.2
Charge
22.3
Insulators and Conductors
22.4
Coulomb’s Law
22.5
The Electric Field
23
The Electric Field
23.2
The Electric Field of Point Charges
23.3
The Electric Field of a Continuous Charge Distribution
23.4
The Electric Fields of Some Common Charge Distributions
23.5
The Parallel-Plate Capacitor
23.6
Motion of a Charged Particle in an Electric Field
23.7
Motion of a Dipole in an Electric Field
24
Gauss’s Law
24.1
Symmetry
24.2
The Concept of Flux
24.3
Calculating Electric Flux
24.4
Gauss’s Law
24.5
Using Gauss’s Law
24.6
Conductors in Electrostatic Equilibrium
25
The Electric Potential
25.1
Electric Potential Energy
25.2
The Potential Energy of Point Charges
25.3
The Potential Energy of a Dipole
25.4
The Electric Potential
25.5
The Electric Potential Inside a Parallel-Plate Capacitor
25.6
The Electric Potential of a Point Charge
25.7
The Electric Potential of Many Charges
26
Potential and Field
26.1
Connecting Potential and Field
26.2
Finding the Electric Field from the Potential
26.4
Sources of Electric Potential
26.5
Capacitance and Capacitors
26.6
The Energy Stored in a Capacitor
26.7
Dielectrics
27
Current and Resistance
27.1
The Electron Current
27.2
Creating a Current
27.3
Current and Current Density
27.4
Conductivity and Resistivity
27.5
Resistance and Ohm’s Law
28
Fundamentals of Circuits
28.1
Circuit Elements and Diagrams
28.2
Kirchhoff’s Laws and the Basic Circuit
28.3
Energy and Power
28.4
Series Resistors
28.5
Real Batteries
28.6
Parallel Resistors
28.8
Getting Grounded
28.9
RC Circuits
29
The Magnetic Field
29.3
The Source of the Magnetic Field: Moving Charges
29.4
The Magnetic Field of a Current
29.5
Magnetic Dipoles
29.6
Ampère’s Law and Solenoids
29.7
The Magnetic Force on a Moving Charge
29.8
Magnetic Forces on Current-Carrying Wires
29.9
Forces and Torques on Current Loops
30
Electromagnetic Induction
30.10
LR Circuits
30.2
Motional emf
30.3
Magnetic Flux
30.4
Lenz’s Law
30.5
Faraday’s Law
30.6
Induced Fields
30.7
Induced Currents: Three Applications
30.8
Inductors
30.9
LC Circuits
31
Electromagnetic Fields and Waves
31.1
E or B? It Depends on Your Perspective
31.2
The Field Laws Thus Far
31.3
The Displacement Current
31.5
Electromagnetic Waves
31.6
Properties of Electromagnetic Waves
31.7
Polarization
32
AC Circuits
32.1
AC Sources and Phasors
32.2
Capacitor Circuits
32.3
RC Filter Circuits
32.4
Inductor Circuits
32.5
The Series RLC Circuit
32.6
Power in AC Circuits
33
Wave Optics
33.2
The Interference of Light
33.3
The Diffraction Grating
33.4
Single-Slit Diffraction
33.5
A Closer Look at Diffraction
33.6
Circular-Aperture Diffraction
33.8
Interferometers
34
Ray Optics
34.1
The Ray Model of Light
34.2
Reflection
34.3
Refraction
34.4
Image Formation by Refraction at a Plane Surface
34.5
Thin Lenses: Ray Tracing
34.6
Thin Lenses: Refraction Theory
34.7
Image Formation with Spherical Mirrors
35
Optical Instruments
35.1
Lenses in Combination
35.2
The Camera
35.3
Vision
35.4
Optical Systems That Magnify
35.5
Color and Dispersion
35.6
The Resolution of Optical Instruments
36
Relativity
36.10
Relativistic Energy
36.2
Galilean Relativity
36.3
Einstein’s Principle of Relativity
36.4
Events and Measurements
36.5
The Relativity of Simultaneity
36.6
Time Dilation
36.7
Length Contraction
36.8
The Lorentz Transformations
36.9
Relativistic Momentum
37
The Foundations of Modern Physics
37.2
The Emission and Absorption of Light
37.3
Cathode Rays and X Rays
37.4
The Discovery of the Electron
37.5
The Fundamental Unit of Charge
37.6
The Discovery of the Nucleus
37.7
Into the Nucleus
38
Quantization
38.1
The Photoelectric Effect
38.2
Einstein’s Explanation
38.3
Photons
38.4
Matter Waves and Energy Quantization
38.5
Bohr’s Model of Atomic Quantization
38.6
The Bohr Hydrogen Atom
38.7
The Hydrogen Spectrum
39
Wave Functions and Uncertainty
39.1
Waves, Particles, and the Double-Slit Experiment
39.2
Connecting the Wave and Photon Views
39.3
The Wave Function
39.4
Normalization
39.5
Wave Packets
39.6
The Heisenberg Uncertainty Principle
40
One-Dimensional Quantum Mechanics
40.10
Quantum-Mechanical Tunneling
40.3
A Particle in a Rigid Box: Energies and Wave Functions
40.4
A Particle in a Rigid Box: Interpreting the Solution
40.6
Finite Potential Wells
40.7
Wave-Function Shapes
40.8
The Quantum Harmonic Oscillator
40.9
More Quantum Models
41
Atomic Physics
41.1
The Hydrogen Atom: Angular Momentum and Energy
41.2
The Hydrogen Atom: Wave Functions and Probabilities
41.3
The Electron’s Spin
41.4
Multielectron Atoms
41.5
The Periodic Table of the Elements
41.6
Excited States and Spectra
41.7
Lifetimes of Excited States
41.8
Stimulated Emission and Lasers
42
Nuclear Physics
42.1
Nuclear Structure
42.2
Nuclear Stability
42.3
The Strong Force
42.4
The Shell Model
42.5
Radiation and Radioactivity
42.6
Nuclear Decay Mechanisms
42.7
Biological Applications of Nuclear Physics
Textbook Solutions for Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Global Edition)
Chapter 4.2 Problem 13
Question
A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in FIGURE EX4.13. The ball's position is shown at 1 s intervals until t = 3 s. At t = 1 s, the ball's velocity is \(\vec{v}\) = (\(2.0 \hat{\imath}\) + \(2.0 \hat{\jmath}\)) m/s.
a. Determine the ball's velocity at t = 0 s, 2 s, and 3 s.
b. What is the value of g on Planet Exidor?
c. What was the ball's launch angle?
Solution
The first step in solving 4.2 problem number trying to solve the problem we have to refer to the textbook question: A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in FIGURE EX4.13. The ball's position is shown at 1 s intervals until t = 3 s. At t = 1 s, the ball's velocity is \(\vec{v}\) = (\(2.0 \hat{\imath}\) + \(2.0 \hat{\jmath}\)) m/s.a. Determine the ball's velocity at t = 0 s, 2 s, and 3 s.b. What is the value of g on Planet Exidor?c. What was the ball's launch angle?
From the textbook chapter Projectile Motion you will find a few key concepts needed to solve this.
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full solution
Title
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Global Edition) 5
Author
Randall D. Knight
ISBN
9781292438221
A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in FIGURE EX4.13. The ball's position is shown at 1 s intervals until t = 3 s. At t = 1 s, the ball's velocity is \(\vec{v}\) = (\(2.0 \hat{\imath}\) + \(2.0 \hat{\jmath}\)) m/s. a. Determine the ball's velocity at t = 0 s, 2 s, and 3 s. b. What is the value of g on Planet Exidor? c. What was the ball's launch angle?
Chapter 4.2 textbook questions
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Chapter 4: Problem 11 Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Global Edition) 5
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Chapter 4: Problem 12 Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Global Edition) 5
A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 80 m above the glacier at a speed of 100 m/s. How far short of the target should it drop the package?
Read more -
Chapter 4: Problem 13 Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Global Edition) 5
A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in FIGURE EX4.13. The ball's position is shown at 1 s intervals until t = 3 s. At t = 1 s, the ball's velocity is \(\vec{v}\) = (\(2.0 \hat{\imath}\) + \(2.0 \hat{\jmath}\)) m/s. a. Determine the ball's velocity at t = 0 s, 2 s, and 3 s. b. What is the value of g on Planet Exidor? c. What was the ball's launch angle?
Read more -
Chapter 4: Problem 14 Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Global Edition) 5
In the Olympic shotput event, an athlete throws the shot with an initial speed of 12.0 m/s at a \(40.0^{\circ}\) angle from the horizontal. The shot leaves her hand at a height of 1.80 m above the ground. How far does the shot travel?
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Chapter 4: Problem 15 Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Global Edition) 5
A rifle is aimed horizontally at a target 40 m away. The bullet hits 1 cm below the target. a. What was the bullet’s flight time? b. What was the bullet’s speed as it left the barrel?
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Chapter 4: Problem 16 Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Global Edition) 5
A friend of yours is a baseball player and wants to determine his pitching speed. You have him stand on a ledge and throw the ball horizontally from an elevation of 6 m above the ground. The ball lands 40 m away. What is his pitching speed?
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Chapter 4: Problem 17 Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Global Edition) 5
On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed of 25 m/s at an angle \(30^{\circ}\) above the horizontal. a. How much farther did the ball travel on the moon than it would have on earth? b. For how much more time was the ball in flight?
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