Relative Motion PDF

1.6 Relative Motion Learning Goal: Solve relative motion problems in two dimensions. A frame of reference is a coordinate system relative to which motion is described or observed. The velocity of an object relative to a specific frame of reference is called the relative velocity.  Ex...

1.6 Relative Motion Learning Goal: Solve relative motion problems in two dimensions. A frame of reference is a coordinate system relative to which motion is described or observed. The velocity of an object relative to a specific frame of reference is called the relative velocity.  Example 1: Passengers on a cruise ship are playing shuffleboard. The shuffleboard disc's velocity relative to the ship is 4.2 m/s [fwd], and the ship is traveling in the same direction as the disc at 4.6 km/h relative to Earth when the water is stationary. a) Determine the disc's velocity relative to Earth. (5.5 m/s [fwd]) b) Determine the disc's velocity relative to Earth when the disc is moving in a direction opposite to that of the ship. (2.9 m/s [bkwd])  Example 2: A boat is heading due north as it crosses a wide river. The velocity of the boat is 10.0 km/h relative to the water. The river has a uniform velocity of 5.00 km/h due east. Determine the boat's velocity relative to an observer on the riverbank. (11.2 km/h [N 26.6° E]) Example 3: A rowboat that can travel 1.5 m/s in still water is travelling east across a river with the water flowing south at a speed of 1.0 m/s. If the river is 100 m wide, a. What is the velocity of the boat with respect to the water? b. What is the velocity of the water with respect to the ground? c. What is the velocity of the boat with respect to the ground? d. How long does the trip take? e. Where does the boat land with respect to the launch point? f. If the passenger really wants to arrive directly across from the launch point, what heading must be taken?  Example 4: The air velocity of a small plane is 230 km/h [N 35 E] when the wind is blowing at 75 km/h [W 25 S]. Determine the velocity of the plane relative to the ground. (170 km/h [E 68 N]) Example 5: An airplane with a wind speed of 250 km/h is heading N70 E in a 50 km/h wind that is travelling N20 E. What is the velocity of the plane with respect to the ground? (280 km/h [N62 E] If the pilot wants to arrive directly north, what heading must be taken? ([N4 W] Example 6: A pilot is required to fly directly from London to Rome in 3.5 hrs. The displacement is 1.4x103 km [S43 E]. A wind is blowing with a velocity of 75 km/h [S]. Determine the required velocity of the plane relative to the air. (350 km/h [S51 E])