>> Hello class Professor Anderson here. Let's take a look at an example problem of a boat crossing a river. This is one of the relative motion problems and let's say that we have the following scenario. We have a river that is flowing in this direction, here's our river and we'll call that speed of the river VRE speed of the river relative to the earth and now we got a boat here and we want our boat to go straight across the river. If our boat's going to go straight across the river should I point my boat directly across the river? What do you guys think? Probably not right everybody knows that if you point it straight across the river the river is going to carry it down stream. So we can't point our boat in that direction, we in fact have to point our boat up stream in this direction. Ok and we need to figure out what direction I need to point the boat and how fast do I have to move the boat in order to get straight across the river. Ok so here's our two relative velocities. We have the velocity of the river relative to the earth and the velocity of the boat relative to the river and let's give you some numbers. Let's say that the speed of the river relative to the earth is 5 kilometers per hour and it is heading east and the velocity of the boat relative to the river the maximum speed that it can do is 10 kilometers per hour but we don't know what the angle is yet. Ok so RV means river relative to earth, VR means boat relative to river and we want to find what is the speed of the boat relative to the earth and at what angle do we need to orientate it, namely this angle right here. Ok and the goal is to go straight across the river, that's the caveat here. Ok there's a couple of different ways to think about this problem but one way to think about it is the following: We can just draw some vectors, this is the vector of the boat relative to the river, this is the river relative to the earth, and if I add those two up it looks like I will get the velocity of the boat relative to the earth. This is a right angle, this is our angle theta and I think that's just about all of the information we need. And now look we've drawn a triangle we know that Pythagoras holds for this right triangle, we've got a 5, we've got a 10, we can solve this for VBE. VBR squared equals VRE squared plus VBE squared and now we can solve this for VBE. VBE equals square root of VBR squared minus VRE squared and we know all of those numbers right? We've got 10 squared, we're going to subtract 5 squared, that's the square root of 75, and we did this earlier, square root of 75 was 8.66 kilometers per hour. Alright, so that's the first part. Before we think about the second part theta, is there some other way we could do this problem? Anybody have another thought on how to do this problem? [ pause in speaking ] Anybody? Ok Ian yeah what do you think how else could we do this problem? >> I would use trigonometry. >> Ok so what would you do with trigonometry? >> I would take the velocity of the boat relative to the river and either use sine or cosine. >> Ok, excellent idea, let's try that. >> Ok so Ian's suggesting that we go back to the original picture and we do a little trig using sines or cosines. Let's try that. Right. VBR is pointing up like that, which means there's two components to it right? There's some component in that direction-VBR we'll call it Y and there is some component in that direction-VBRX. This one is of course the sine component if this is theta, this one is the cosine component so this is VBR sine of theta, this is going to be VBR cosine of theta and if we're just thinking about speeds there you can go like that. Alright, if I'm pointing this thing slightly up stream then my component here up stream has to be what if I'm going to end up moving straight across the river? It has to be exactly the speed of the river right? And whatever the component of the velocity of the boat going up stream that has to exactly match a component of the river going down stream and so our condition now is the following: VBRX has to equal the speed of the river going down stream. That makes sense right? If I turn my boat all the way up stream such that I was going up stream at 5 kilometers per hour and the river is going down stream at 5 kilometers per hour, I wouldn't go anywhere right? We would be exactly still and so whatever component I have going up stream as long as it equals the velocity of the river, the speed of the river, then any remaining vertical component is just going to carry me straight across the river. Alright, so look we've got VBR times the sine of theta equals VRE and now you can calculate theta. Theta is the arc sine of VRE over VBR and so using trig it allowed us to in fact first get theta and once you get theta then you can go back and calculate this quantity VBE the velocity of the boat going across the river. Ok hopefully that's clear and if you want to plug in the numbers you can double check my answer. We've got a theta of I think 30 degrees. Ok any questions about that one? Alright, if that's not clear come see me in office hours. Cheers.
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:
8mPlay a video:
Related Videos
Related Practice