1. A balloon is floating in a constant-speed wind blowing from left to right at a rate of 5 m/s.
- The balloon’s velocity relative to the ground: 5 m/s to the right
- The balloon’s velocity relative to the air: 0 m/s
- The air’s velocity relative to the ground: 5 m/s to the right
2. A person is walking on a moving sidewalk that moves at 2 m/s to the right. The person walks at 1 m/s to the right relative to the sidewalk.
- The person’s velocity relative to the ground: 3 m/s to the right
- The person’s velocity relative to the sidewalk: 1 m/s to the right
- The sidewalk’s velocity relative to the ground: 2 m/s to the right
3. A boat is moving downstream in a river. The river flows at 3 m/s to the right. The boat moves at 4 m/s to the right relative to the water.
- The boat’s velocity relative to the ground: 7 m/s to the right
- The boat’s velocity relative to the water: 4 m/s to the right
- The water’s velocity relative to the ground: 3 m/s to the right
4. A car is driving north at 60 km/h. A truck is driving east at 80 km/h. What is the velocity of the car relative to the truck?
- The car’s velocity relative to the truck: 100 km/h at 36.9° west of north (or 53.1° north of west)
5. An airplane is flying due east at 200 m/s relative to the air. The wind is blowing due north at 50 m/s. What is the airplane’s velocity relative to the ground?
- The airplane’s velocity relative to the ground: 206.2 m/s at 14.0° north of east
6. A swimmer can swim at 2 m/s in still water. The river current flows at 1 m/s to the right. The swimmer wants to cross the river directly from south to north.
- The swimmer must aim upstream at an angle θ where sin(θ) = 1/2, so θ = 30° west of north.
- The swimmer’s speed relative to the ground while crossing: √3 m/s north
7. Two cars are moving on perpendicular roads. Car A moves east at 30 m/s. Car B moves north at 40 m/s. What is the velocity of Car A relative to Car B?
- The velocity of Car A relative to Car B: 50 m/s at 53.1° south of east (or 36.9° east of south)
8. A jet is flying at 300 m/s due east relative to the air. The wind is blowing at 50 m/s due south. What is the jet’s velocity relative to the ground?
- The jet’s velocity relative to the ground: 304.1 m/s at 9.5° south of east
9. A person is walking north at 2 m/s on a train moving east at 10 m/s. What is the person’s velocity relative to the ground?
- The person’s velocity relative to the ground: 10.2 m/s at 11.3° north of east
10. A boat crosses a river flowing at 2 m/s to the right. The boat’s speed relative to the water is 4 m/s. If the boat points directly across the river (north), what is its velocity relative to the ground?
- The boat’s velocity relative to the ground: 4.47 m/s at 26.6° north of east
Parent Tip: Review the logic above to help your child master the concept of related rates worksheet.
