# Kinematics in Two Dimensions

## Problems

### practice

- I went for a walk one day. I walked north 6.0 km at 6.0 km/h and then west 10 km at 5.0 km/hr. (This problem is deceptively easy, so be careful. Begin each part by reviewing the appropriate physical definition.) Determine…
- the total distance of the entire trip
- the total displacement of the entire trip
- the average speed of the entire trip
- the average velocity of the entire trip
- the average acceleration of the entire trip

- A swimmer heads directly across a river swimming at 1.6 m/s relative to still water. She arrives at a point 40 m downstream from the point directly across the river, which is 80 m wide. Determine…
- the speed of the current
- the magnitude of the swimmer's resultant velocity
- the direction of the swimmer's resultant velocity
- the time it takes the swimmer to cross the river

- A car enters an intersection at 20 m/s where it collides with a truck. The impact rotates the car 90° and gives it a speed of 15 m/s. Determine the average acceleration of the car if it was in contact with the truck for 1.25 s.
- The asteroid 2007 VK184 is classified as a near earth object (NEO). It has an orbit that brings it close enough to earth, often enough that we need to be concerned. It will make 7 close approaches in the 21st century. The first occured in 2007 when the asteroid was discovered (thus the provisional name 2007 VK184). The last will be in 2048 when there is a small but non-zero probability (< 1%) of collision with the Earth. This is the only asteroid currently known to pose a threat to the Earth in this century. On 30 May 2048 at 22:11 UTC (6:11 PM New York time), asteroid 2007 VK184 will be traveling at an estimated 16.9401 km/s relative to the sun. If it strikes the Earth, the speed of impact would be 16.9436 km/s (Source: JPL). Determine the impact angle between the velocity vectors of the Earth and the asteroid.

### conceptual

- At what direction (somewhat upstream, directly across, or somewhat downstream) should you swim in order to cross a river…
- with the least displacement?
- in the least time?

### numerical

- In the fictitious city of Metropolis, streets run east-west while avenues run north-south. The separation between centers for both the streets and the avenues is 100 m, resulting in square city blocks. Superman is located at 33rd Street and 3rd Avenue while Lois Lane is located north and east of Superman at 45th Street and 12th Avenue.
- How far would Lois Lane have to walk to reach Superman?
- How far would Superman have to fly to reach Lois Lane?
- In what direction should Superman fly to reach Lois Lane as quickly as possible?

- Calculate both the distance and the magnitude of the displacement of the Earth after…
- one complete orbit around the sun
- one-half orbit around the sun
- one-fourth orbit around the sun
- What relationship between distance and displacement does this illustrate?

- Calculate both the speed and the magnitude of the velocity of the Earth after completing…
- one complete orbit around the sun
- one-half orbit around the sun
- one-fourth orbit around the sun
- What relationship between speed and velocity does this verify?

- A flight from Portland, Oregon to New York City takes 5 hours and 20 minutes. The return flight takes 6 hours and 30 minutes. The airport to airport distance is 3949 km. Determine…
- the average speed of the initial flight
- the average speed of the return flight
- the average speed and direction of the wind

- A girl rides her bicycle 1.60 km north, 0.80 km east, and 0.40 km south in 14 minutes.
- Sketch the path taken by the girl. Draw the vector representing the resultant displacement of the girl for the entire bicycle trip
- Determine the magnitude of the girl's resultant displacement for the entire bicycle trip, in kilometers.
- Determine the measure of the angle, in degrees, between the resultant and the 1.60 km displacement vector.
- Calculate the girl's average speed for the entire bicycle trip.

- A river has a current flowing with a velocity of 1.0 meters per second due south. A boat is 50 meters from the east riverbank. It travels at 2.0 meters per second relative to the river and is headed due east.
- Sketch the components of the boat's velocity. Add a vector representing the resultant velocity of the boat.
- Determine the angle, in degrees, between the boat's resultant velocity and due east.
- Determine the magnitude of the boat's resultant velocity.
- Calculate the time required for the boat to cross the river.

### algebraic

- Given a straight river with parallel banks flowing uniformly at speed
*v*and a swimmer capable of speed_{river}*v*>_{swim}*v*at what angle (assuming that directly across is 0°) should the swimmer head in order to cross the river…_{river}- with the least displacement,
- in the least time?