>> Hello, class. Professor Anderson here. Let's talk about a problem where you are swimming across the river. And we need to figure out something about the motion as you cross the river. And let's say that the following applies. Here's one bank of the river. Here's the other bank of the river. And we know that this distance across the river has some particular value. We'll call it d1. As you swim across the river, you're going to end up downstream and, in fact, we know that distance, d2. And we also know a couple more things. We know the velocity of the river is in that direction. And we know that you are going to point yourself in that direction and swim. So, let's put some numbers in here. Let's say that d1 is 200 meters. D2 is 150 meters. And let's say that the velocity of the river relative to the Earth is 5 meters per second. OK? And now let's see if we can figure out a couple things. We need to figure out how fast you need to swim and at what angle, theta, you should point yourself. All right. This looks like a difficult problem. Has anybody looked at this problem? Yeah. OK. If you have some thoughts on what we should do next, give me some instruction. What should we do next here? Right? We've got a picture. We've got a bunch of givens. What should we do next? >> Doug? >> Find out how long it's going to take to cross the river. >> Find out how long it's going to take to cross the river. I like that. All right. How long to cross the river. So, how do we do that? Doug, what do you think? >> Probably use one of the kinematic equations? >> Excellent. It's almost like it's related to early in the lectures. Maybe. All right. Let's use one of the kinematic equations. So, one of our kinematic equations looks like this. Y-final equals y-initial plus vy-initial times t plus 1/2a-sub-y t-squared. That looks like a good one. Any time we write down a kinematic equation, we should immediately say, "Oh, we need a coordinate system." Let's put our origin right there. We'll say x is to the right and we'll say y is up. And if we do that, then we can simplify this equation quite a bit because what is y-final equal to in this case? y-final is just equal to d1. Y-initial is where we started, which is zero. dy-initial, we're not really sure about that yet. A is zero. OK? That's one of our givens. We're going to say that there's no acceleration in this problem. OK? It's just constant velocity motion. All right. So, it seems like we might have enough. But let's take a look at it and double check. OK. So, let's take a look at this equation right here. We've got d1 equal vy-initial times t. That looks like we might be able to solve that for t. Except, what is vy-initial? Vy-initial is how fast is the swimmer going in this vertical direction, in this y direction? OK? We don't know what that is, but what we do know is if this is the speed of the swimmer in that direction, then vy-initial is right there. OK? And this is a right triangle. And so we can say vy-initial is just equal to the speed of the swimmer relative to the river times the cosine of theta. All right. So, we have one equation now, d1 equals vsr cosine theta. All of that times t. All right. But we're not quite there yet. It seems like we're going to have to worry about the x equations. So, let's try this again, but use the x variables. x-final equals x-initial plus vx-initial times t plus 1/ a-sub-x t squared. All right. x-initial is zero. X-final is going to be d2. vx-initial, we're not exactly sure yet. There's no acceleration so that is zero. All right. So, we get d2 equals vx-i times t. And now we have to think about this vx-i. OK? We just drew a triangle up here, which had the swimmer. And this was v of the swimmer in the x direction. But that's not the only thing moving in the x direction. The swimmer has some component of that way, but the river has some component that way. And so, in fact, we need to subtract the two. It's going to be v-river relative to the Earth minus this component, v-swimmer relative to the river times sine of theta. And all of that multiplying t. All right. Seems like we are almost there. Right? Now we have an equation for d1. We have an equation for d2. And there's one more thing that we do know is you can calculate this distance, which is just the sum of the squares, square root. All right. So, with this information, hopefully it's enough to figure out the problem. OK? I'm not going to do it since it's one of your homework problems explicitly. But this is sort of how you set up the problem. OK? Any questions about this? Any time you're faced with these relative motion problems, always break it down into x and y and think about which ones you need to add or subtract in terms of the vector. All right. Hopefully that's clear. If not, come see me in office hours.
Table of contents
- 0. Math Review31m
- 1. Intro to Physics Units1h 23m
- 2. 1D Motion / Kinematics3h 56m
- Vectors, Scalars, & Displacement13m
- Average Velocity32m
- Intro to Acceleration7m
- Position-Time Graphs & Velocity26m
- Conceptual Problems with Position-Time Graphs22m
- Velocity-Time Graphs & Acceleration5m
- Calculating Displacement from Velocity-Time Graphs15m
- Conceptual Problems with Velocity-Time Graphs10m
- Calculating Change in Velocity from Acceleration-Time Graphs10m
- Graphing Position, Velocity, and Acceleration Graphs11m
- Kinematics Equations37m
- Vertical Motion and Free Fall19m
- Catch/Overtake Problems23m
- 3. Vectors2h 43m
- Review of Vectors vs. Scalars1m
- Introduction to Vectors7m
- Adding Vectors Graphically22m
- Vector Composition & Decomposition11m
- Adding Vectors by Components13m
- Trig Review24m
- Unit Vectors15m
- Introduction to Dot Product (Scalar Product)12m
- Calculating Dot Product Using Components12m
- Intro to Cross Product (Vector Product)23m
- Calculating Cross Product Using Components17m
- 4. 2D Kinematics1h 42m
- 5. Projectile Motion3h 6m
- 6. Intro to Forces (Dynamics)3h 22m
- 7. Friction, Inclines, Systems2h 44m
- 8. Centripetal Forces & Gravitation7h 26m
- Uniform Circular Motion7m
- Period and Frequency in Uniform Circular Motion20m
- Centripetal Forces15m
- Vertical Centripetal Forces10m
- Flat Curves9m
- Banked Curves10m
- Newton's Law of Gravity30m
- Gravitational Forces in 2D25m
- Acceleration Due to Gravity13m
- Satellite Motion: Intro5m
- Satellite Motion: Speed & Period35m
- Geosynchronous Orbits15m
- Overview of Kepler's Laws5m
- Kepler's First Law11m
- Kepler's Third Law16m
- Kepler's Third Law for Elliptical Orbits15m
- Gravitational Potential Energy21m
- Gravitational Potential Energy for Systems of Masses17m
- Escape Velocity21m
- Energy of Circular Orbits23m
- Energy of Elliptical Orbits36m
- Black Holes16m
- Gravitational Force Inside the Earth13m
- Mass Distribution with Calculus45m
- 9. Work & Energy1h 59m
- 10. Conservation of Energy2h 54m
- Intro to Energy Types3m
- Gravitational Potential Energy10m
- Intro to Conservation of Energy32m
- Energy with Non-Conservative Forces20m
- Springs & Elastic Potential Energy19m
- Solving Projectile Motion Using Energy13m
- Motion Along Curved Paths4m
- Rollercoaster Problems13m
- Pendulum Problems13m
- Energy in Connected Objects (Systems)24m
- Force & Potential Energy18m
- 11. Momentum & Impulse3h 40m
- Intro to Momentum11m
- Intro to Impulse14m
- Impulse with Variable Forces12m
- Intro to Conservation of Momentum17m
- Push-Away Problems19m
- Types of Collisions4m
- Completely Inelastic Collisions28m
- Adding Mass to a Moving System8m
- Collisions & Motion (Momentum & Energy)26m
- Ballistic Pendulum14m
- Collisions with Springs13m
- Elastic Collisions24m
- How to Identify the Type of Collision9m
- Intro to Center of Mass15m
- 12. Rotational Kinematics2h 59m
- 13. Rotational Inertia & Energy7h 4m
- More Conservation of Energy Problems54m
- Conservation of Energy in Rolling Motion45m
- Parallel Axis Theorem13m
- Intro to Moment of Inertia28m
- Moment of Inertia via Integration18m
- Moment of Inertia of Systems23m
- Moment of Inertia & Mass Distribution10m
- Intro to Rotational Kinetic Energy16m
- Energy of Rolling Motion18m
- Types of Motion & Energy24m
- Conservation of Energy with Rotation35m
- Torque with Kinematic Equations56m
- Rotational Dynamics with Two Motions50m
- Rotational Dynamics of Rolling Motion27m
- 14. Torque & Rotational Dynamics2h 5m
- 15. Rotational Equilibrium3h 39m
- 16. Angular Momentum3h 6m
- Opening/Closing Arms on Rotating Stool18m
- Conservation of Angular Momentum46m
- Angular Momentum & Newton's Second Law10m
- Intro to Angular Collisions15m
- Jumping Into/Out of Moving Disc23m
- Spinning on String of Variable Length20m
- Angular Collisions with Linear Motion8m
- Intro to Angular Momentum15m
- Angular Momentum of a Point Mass21m
- Angular Momentum of Objects in Linear Motion7m
- 17. Periodic Motion2h 9m
- 18. Waves & Sound3h 40m
- Intro to Waves11m
- Velocity of Transverse Waves21m
- Velocity of Longitudinal Waves11m
- Wave Functions31m
- Phase Constant14m
- Average Power of Waves on Strings10m
- Wave Intensity19m
- Sound Intensity13m
- Wave Interference8m
- Superposition of Wave Functions3m
- Standing Waves30m
- Standing Wave Functions14m
- Standing Sound Waves12m
- Beats8m
- The Doppler Effect7m
- 19. Fluid Mechanics2h 27m
- 20. Heat and Temperature3h 7m
- Temperature16m
- Linear Thermal Expansion14m
- Volume Thermal Expansion14m
- Moles and Avogadro's Number14m
- Specific Heat & Temperature Changes12m
- Latent Heat & Phase Changes16m
- Intro to Calorimetry21m
- Calorimetry with Temperature and Phase Changes15m
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes9m
- Phase Diagrams, Triple Points and Critical Points6m
- Heat Transfer44m
- 21. Kinetic Theory of Ideal Gases1h 50m
- 22. The First Law of Thermodynamics1h 26m
- 23. The Second Law of Thermodynamics3h 11m
- 24. Electric Force & Field; Gauss' Law3h 42m
- 25. Electric Potential1h 51m
- 26. Capacitors & Dielectrics2h 2m
- 27. Resistors & DC Circuits3h 8m
- 28. Magnetic Fields and Forces2h 23m
- 29. Sources of Magnetic Field2h 30m
- Magnetic Field Produced by Moving Charges10m
- Magnetic Field Produced by Straight Currents27m
- Magnetic Force Between Parallel Currents12m
- Magnetic Force Between Two Moving Charges9m
- Magnetic Field Produced by Loops and Solenoids42m
- Toroidal Solenoids aka Toroids12m
- Biot-Savart Law (Calculus)18m
- Ampere's Law (Calculus)17m
- 30. Induction and Inductance3h 37m
- 31. Alternating Current2h 37m
- Alternating Voltages and Currents18m
- RMS Current and Voltage9m
- Phasors20m
- Resistors in AC Circuits9m
- Phasors for Resistors7m
- Capacitors in AC Circuits16m
- Phasors for Capacitors8m
- Inductors in AC Circuits13m
- Phasors for Inductors7m
- Impedance in AC Circuits18m
- Series LRC Circuits11m
- Resonance in Series LRC Circuits10m
- Power in AC Circuits5m
- 32. Electromagnetic Waves2h 14m
- 33. Geometric Optics2h 57m
- 34. Wave Optics1h 15m
- 35. Special Relativity2h 10m
4. 2D Kinematics
Intro to Relative Velocity
Video duration:
7mPlay a video:
Related Videos
Related Practice