1. Two-Dimensional Kinematics
The study of motion in two directions

2. A boat crossing a river

3. 2-Dimensional Motion Maps
For each of the following create a 2- dimensional motion map of the situation, then solve for the requested value. Plot your motion map using an appropriate time scale based on the described motion.

4. 2-Dimensional Motion Map
A plane is flying north at 120 km/h. It is encountering a tail wind of 30km/hr.
How long does it take the plane to fly 600km?
What is the total displacement of the plane?

5. 2-Dimensional Motion Map
A boat is crossing a river that is flowing south with a current of 5m/s. The boat is traveling East and would have a speed of 5m/s in a calm current. If the river is 500m across, how long does it take to cross the river? What is the total displacement of the boat?

6. 2-Dimensional Motion Map
An airplane is traveling north at 300 km/hr. The plane encounters a cross wind blowing west at 50 km/hr. How far north has the plane traveled after 1 hour, 2 hour, 3 hours, 4 hours, 5 hours? How far west has the plane traveled after 1 hour, 2 hour, 3 hours, 4 hours, 5 hours? What is the total displacement of the plane after 1 hour, 2 hour, 3 hours, 4 hours, 5 hours? What is the average velocity of the plane after 1 hour, 2 hour, 3 hours, 4 hours, 5 hours?

7. 2-Dimensional Motion Map
A ball is traveling at 5m/s when it rolls of a cabinet that is 2.5m high. Once it reaches the end of the cabinet, assume it is in free-fall.
How long does it take to reach the ground?
How fast is it traveling vertically when it reaches the floor?
How far from the base of the cabinet will it land?
What is the final velocity of the ball?

8. Challenge Problem: (20pts) 2-Dimensional Motion Map
A plane is taking off from a runway. The plane starts from rest and accelerates at 6.0 m/s2. When the plane reaches a speed of 200. km/hr , the pilot pulls back on the stick causing is to accelerate vertically at 30. m/s2. At this point it will travel horizontally at a constant velocity and accelerate vertically until it reaches a vertical velocity of 150.km/hr. From then on it will maintain a constant velocity in both the horizontal and vertical motions.
How long at a minimum must the runway be to accommodate this take off?
Once the aircraft starts to move, how much time does it take this aircraft to reach an altitude of 1.0km?
How far does it travel horizontally during this time?
What is the total displacement of the aircraft when it reaches an altitude of 1.0km?
What is the final velocity of the plane?

9. 2-Dimensional Motion Map
A cannon is launches a cannonball at 50m/s horizontally from the top of a 50m cliff.
How long does it take to reach the ground?
How fast is it traveling vertically when it reaches the ground?
What is the range of the shot?
What is the impact velocity of the cannonball?

10. 2-Dimensional Motion Map
A football is kicked from a tee with an initial velocity of degrees above the horizontal.
What is the time of flight?
What is the range of the kick?
What is the maximum height reached by the ball?
What is the velocity of the ball when the kick- returner catches the ball?