Relative Velocity Physics 1 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

We will sort this out with the concept of Relative Velocity. When an object is moving, the description of its motion is always tied to a frame of reference. For example, suppose two cars pass by each other, traveling in opposite directions. The description of the cars’ motion will depend on the reference frame of the observer. A person standing by the side of the road will see the motion differently than a person riding in one of the cars. We will sort this out with the concept of Relative Velocity. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

We will sort this out with the concept of Relative Velocity. When an object is moving, the description of its motion is always tied to a frame of reference. For example, suppose two cars pass by each other, traveling in opposite directions. The description of the cars’ motion will depend on the reference frame of the observer. A person standing by the side of the road will see the motion differently than a person riding in one of the cars. We will sort this out with the concept of Relative Velocity. Suppose the cars are both traveling at a speed of 50mph, and there is an observer standing by the side of the road. Here is a diagram, drawn from the point of view of the observer. Car B Car A vB/person = 50mph vA/person = -50mph The stated velocities are for one object relative to the other. What would you write down for the velocity of car B relative to car A? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

We will sort this out with the concept of Relative Velocity. When an object is moving, the description of its motion is always tied to a frame of reference. For example, suppose two cars pass by each other, traveling in opposite directions. The description of the cars’ motion will depend on the reference frame of the observer. A person standing by the side of the road will see the motion differently than a person riding in one of the cars. We will sort this out with the concept of Relative Velocity. Suppose the cars are both traveling at a speed of 50mph, and there is an observer standing by the side of the road. Here is a diagram, drawn from the point of view of the observer. Car B Car A vB/person = 50mph vA/person = -50mph The stated velocities are for one object relative to the other. What would you write down for the velocity of car B relative to car A? vB/A = 100mph Note that we can calculate this from the observer info: vB/A = vB/person – vA/person = (50mph) – (-50mph) = 100mph Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Find the following relative velocities: vwoman/floor vman/floor Let’s try another example. Airport terminals have moving walkways to help travelers get around more quickly. In our example there will be two moving walkways going in opposite directions, both at a speed of 1.5 m/s (relative to the floor, which is not moving). Suppose the people in the picture would be walking at a speed of 2.0 m/s if they were on the stationary floor. The woman in the picture (closer to us) is facing the wrong way on her walkway, and the man (farther) is facing the correct direction. Find the following relative velocities: vwoman/floor vman/floor vman/woman Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Find the following relative velocities: vwoman/floor = 0.5 m/s Let’s try another example. Airport terminals have moving walkways to help travelers get around more quickly. In our example there will be two moving walkways going in opposite directions, both at a speed of 1.5 m/s (relative to the floor, which is not moving). Suppose the people in the picture would be walking at a speed of 2.0 m/s if they were on the stationary floor. The woman in the picture (closer to us) is facing the wrong way on her walkway, and the man (farther) is facing the correct direction. Find the following relative velocities: vwoman/floor = 0.5 m/s vman/floor = 3.5 m/s vman/woman = ? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

vman/woman = vman/floor – vwoman/floor Let’s try another example. Airport terminals have moving walkways to help travelers get around more quickly. In our example there will be two moving walkways going in opposite directions, both at a speed of 1.5 m/s (relative to the floor, which is not moving). Suppose the people in the picture would be walking at a speed of 2.0 m/s if they were on the stationary floor. The woman in the picture (closer to us) is facing the wrong way on her walkway, and the man (farther) is facing the correct direction. Find the following relative velocities: vwoman/floor = 0.5 m/s vman/floor = 3.5 m/s vman/woman = 3.0 m/s vman/woman = vman/floor – vwoman/floor Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Find the following relative velocities: vwoman/floor = 0.5 m/s Let’s try another example. Airport terminals have moving walkways to help travelers get around more quickly. In our example there will be two moving walkways going in opposite directions, both at a speed of 1.5 m/s (relative to the floor, which is not moving). Suppose the people in the picture would be walking at a speed of 2.0 m/s if they were on the stationary floor. The woman in the picture (closer to us) is facing the wrong way on her walkway, and the man (farther) is facing the correct direction. Find the following relative velocities: vwoman/floor = 0.5 m/s vman/floor = 3.5 m/s vman/woman = 3.0 m/s How fast would the woman have to walk (run!) to keep up with the man? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Find the following relative velocities: vwoman/floor = 0.5 m/s Let’s try another example. Airport terminals have moving walkways to help travelers get around more quickly. In our example there will be two moving walkways going in opposite directions, both at a speed of 1.5 m/s (relative to the floor, which is not moving). Suppose the people in the picture would be walking at a speed of 2.0 m/s if they were on the stationary floor. The woman in the picture (closer to us) is facing the wrong way on her walkway, and the man (farther) is facing the correct direction. Find the following relative velocities: vwoman/floor = 0.5 m/s vman/floor = 3.5 m/s vman/woman = 3.0 m/s How fast would the woman have to walk (run!) to keep up with the man? 5 m/s. She would have to go 3 m/s faster than she was before to make up for their relative velocity. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Walking at 1 m/s Standing at rest The concept of relative velocity can be generalized to 2 or 3 dimensions by using the same ideas, but with vector velocities instead. Let’s work through a typical example: A man observes snow falling vertically when he is at rest, but when he walks at a speed of 1 m/s, the snow appears to be falling at an angle of 30° relative to the vertical. Find the speed of the snow relative to the earth. Standing at rest Walking at 1 m/s Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Walking at 1 m/s Standing at rest The concept of relative velocity can be generalized to 2 or 3 dimensions by using the same ideas, but with vector velocities instead. Let’s work through a typical example: A man observes snow falling vertically when he is at rest, but when he walks at a speed of 1 m/s, the snow appears to be falling at an angle of 30° relative to the vertical. Find the speed of the snow relative to the earth. Standing at rest vm/e = 0 30° vs/m vs/e vs/e ve/m Walking at 1 m/s vm/e = 1 m/s Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

tan 30° = 1 𝑚 𝑠 𝑣 𝑠/𝑒 𝑣 𝑠/𝑒 =1.7 𝑚 𝑠 Walking at 1 m/s Standing at rest The concept of relative velocity can be generalized to 2 or 3 dimensions by using the same ideas, but with vector velocities instead. Let’s work through a typical example: A man observes snow falling vertically when he is at rest, but when he walks at a speed of 1 m/s, the snow appears to be falling at an angle of 30° relative to the vertical. Find the speed of the snow relative to the earth. Standing at rest vm/e = 0 We can use the triangle in the diagram to find the speed. tan 30° = 1 𝑚 𝑠 𝑣 𝑠/𝑒 30° vs/m vs/e 𝑣 𝑠/𝑒 =1.7 𝑚 𝑠 vs/e ve/m Walking at 1 m/s vm/e = 1 m/s Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

tan 30° = 1 𝑚 𝑠 𝑣 𝑠/𝑒 𝑣 𝑠/𝑒 =1.7 𝑚 𝑠 𝑣 𝑠/𝑒 + 𝑣 𝑒/𝑚 = 𝑣 𝑠/𝑚 The concept of relative velocity can be generalized to 2 or 3 dimensions by using the same ideas, but with vector velocities instead. Let’s work through a typical example: A man observes snow falling vertically when he is at rest, but when he walks at a speed of 1 m/s, the snow appears to be falling at an angle of 30° relative to the vertical. Find the speed of the snow relative to the earth. Standing at rest vm/e = 0 We can use the triangle in the diagram to find the speed. tan 30° = 1 𝑚 𝑠 𝑣 𝑠/𝑒 30° vs/m vs/e 𝑣 𝑠/𝑒 =1.7 𝑚 𝑠 vs/e Make sure you see how the notation works. ve/m 𝑣 𝑠/𝑒 + 𝑣 𝑒/𝑚 = 𝑣 𝑠/𝑚 Walking at 1 m/s vm/e = 1 m/s Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

One more example. Suppose you can row your boat at a steady speed of 5m/s in still water. If the current is flowing at 3m/s, at what angle should you point to reach the other side of the river directly across from where you started? Let’s start by labeling the vectors in the diagram. Use B for boat, W for water and S for shore. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

One more example. Suppose you can row your boat at a steady speed of 5m/s in still water. If the current is flowing at 3m/s, at what angle should you point to reach the other side of the river directly across from where you started? Let’s start by labeling the vectors in the diagram. Use B for boat, W for water and S for shore. 𝑣 𝑊/𝑆 𝑣 𝐵/𝑊 When we add these vectors together, we get the velocity of the boat with respect to the shore, and we want that to go straight across the river. 𝑣 𝐵/𝑊 + 𝑣 𝑊/𝑆 = 𝑣 𝐵/𝑆 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

One more example. Suppose you can row your boat at a steady speed of 5m/s in still water. If the current is flowing at 3m/s, at what angle should you point to reach the other side of the river directly across from where you started? Let’s start by labeling the vectors in the diagram. Use B for boat, W for water and S for shore. 𝑣 𝑊/𝑆 𝑣 𝐵/𝑊 When we add these vectors together, we get the velocity of the boat with respect to the shore, and we want that to go straight across the river. 𝑣 𝐵/𝑊 + 𝑣 𝑊/𝑆 = 𝑣 𝐵/𝑆 We can use our right triangle rules to find the angle now. 𝑣 𝑊/𝑆 𝑣 𝐵/𝑊 𝜃 𝑣 𝐵/𝑆 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

𝑣 𝐵/𝑊 + 𝑣 𝑊/𝑆 = 𝑣 𝐵/𝑆 sin 𝜃 = 𝑣 𝑊/𝑆 𝑣 𝐵/𝑊 = 3 𝑚 𝑠 5 𝑚 𝑠 𝜃=37° One more example. Suppose you can row your boat at a steady speed of 5m/s in still water. If the current is flowing at 3m/s, at what angle should you point to reach the other side of the river directly across from where you started? Let’s start by labeling the vectors in the diagram. Use B for boat, W for water and S for shore. 𝑣 𝑊/𝑆 𝑣 𝐵/𝑊 When we add these vectors together, we get the velocity of the boat with respect to the shore, and we want that to go straight across the river. 𝑣 𝐵/𝑊 + 𝑣 𝑊/𝑆 = 𝑣 𝐵/𝑆 We can use our right triangle rules to find the angle now. sin 𝜃 = 𝑣 𝑊/𝑆 𝑣 𝐵/𝑊 = 3 𝑚 𝑠 5 𝑚 𝑠 𝑣 𝑊/𝑆 𝑣 𝐵/𝑊 𝜃 𝑣 𝐵/𝑆 𝜃=37° Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB