1.6.1 Inertial Reference Frames

Transcription

1 1.6.1 Inertial Reference Frames The laws of physics which apply when you are at rest on the earth also apply when you are in any reference frame which is moving at a constant velocity with respect to the Earth. Such a reference frame is called an inertial frame of reference. For example, you can toss and catch a ball in a moving bus if the bus moves in a straight line at a constant speed. As soon as the bus turns or accelerates, the reference frame is no longer inertial. The motion of the ball will have a different appearance when viewed from a different reference frame. This can be explained by including the relative velocity of the reference frame in the description of the motion Relative Velocity in One Dimension Eg.#1 A passenger on a train traveling 120 km/hr [N] gets up and travels at 6.0 km/hr [N] with respect to the train. Determine the velocity of the person with respect to the ground. a) What is? b) What is? c) What is? To determine the velocity of the passenger with respect to the ground (symbolized by ), we add the two vectors above. The velocity of the passenger with respect to the ground is 126 km./hr [N] Page 1 of 10

2 1.6.3 Relative Velocity in Two Dimensions The two dimensional relative velocity situations we will describe in this section are: the motion of an airplane in the wind current. the motion of a boat in a water current. Just as we did above, to find the velocity of an object in another reference frame we use the process of vector addition. Eg.#2 A rowboat than can travel 1.5 m/s in still water is traveling 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? b) What is? c) What is? Page 2 of 10

3 d) How long does the trip take? e) Where does the boat land with respect to the launch point? The boat lands 67m. downstream. f) If the passenger really wants to arrive directly across from the launch point, what heading must be taken? o The boater must take a heading of [N48 E] Another situation that involves 2 dimensional relative velocity is an airplane traveling on a windy day. The pilot must make allowances for the wind speed when planning their heading. Page 3 of 10

4 Eg.#3 An airplane with a windspeed of 250 km/hr. is heading N70 E in a 50 km/hr. wind that is traveling N20 E. a) What is? 250km/hr[N70 E] b) What is? 50km/hr [N20 E] c) What is? d) If the pilot wants to arrive directly north, what heading must be taken? o The pilot must use a heading of [N3.9 W] Page 4 of 10

5 Worksheet Something is incorrect in each of the following equations. Rewrite each to show the correction. a) b) c) d) 2. A cruise ship is moving with a velocity of 2.8 m./s.[fwd] relative to the water. A group of tourists walks on the deck with a velocity of 1.1 m./s. relative to the deck. Determine their velocity relative to the water if they are walking toward: a) the bow (front) b) the stern (the back) c) the starboard (right side) Page 5 of 10

6 3. A second cruise ship travels with a velocity of 2.8 m./s.[n] with respect to the water in a place where the water moves with a velocity of 2.4 m./s.[n] with respect to the coast. Find the velocity with respect to the coast of a group of tourists who walk at 1.1 m./s. towards the starboard (right) side of the deck. Page 6 of 10

7 4. An aircraft travelling with a velocity relative to the air of 320 km./hr.[s62 W] passes o over Winnipeg. The wind velocity is 72 km./hr.[s]. Determine the displacement of the plane from Winnipeg 2.0 hrs later. Page 7 of 10

8 5. Two kayakers can move at the same speed in calm water. One begins kayaking straight across a river, while the other kayaks at an angle upstream in the same river to land straight across from the starting point. Assume that the speed of the kayakers is greater than the speed of the river current. Which kayaker reaches the far side first? Explain why. Consider the velocity vector diagram shown. The two kayakers have the same velocity with respect to the water as shown by the two vectors and which are the same length. If we compare the velocities of the two kayakers with respect to the ground, we see that the component of that is directly across the river if greater than the component of that is directly across the river. This means that the first kayaker has a greater speed that is directed across the river so the first kayaker will arrive earlier than the second kayaker. 6. A swimmer who can swim at 0.75 m./s. in still water swims directly north across a river 72 metres wide with water that moves East. The swimmer lands on the north shore at a position 54 m. downstream from the starting point. a) Determine the velocity of the river current. Page 8 of 10

9 b) Determine the swimmer s velocity relative to the shore. c) Determine the direction the swimmer would have to aim to land directly across from the starting position. the swimmer s heading should be: Page 9 of 10

10 7. A pilot is required to fly directly from London, UK to Rome, Italy in 3.5 hrs. The displacement is. A wind is blowing with a velocity of 75 km/hr[s]. Determine the required velocity of the plane relative to the air. Page 10 of 10