Introduction to Mechanics Relative Motion

Transcription

1 Introduction to Mechanics Relative Motion Lana heridan De Anza College Feb 7, 2019

2 Last time motion in 2 dimensions relative motion

3 Overview relative motion examples

4 Relative Motion Example v BA dt A boat crossing a wide river frame moves B, which with moves ato speed the right of 10.0 km/h with a constant velocity relative to the water. The water in the river v BA. The has a uniform speed of vector r PA is the particle s position 5.00 km/h due east relative vector relative the Earth. to A, and If r Pthe B is its boat heads due position vector relative to north, determine the velocity of the boat relative B. to an observer standing on either bank. 1 ketch: ore, we conclude that a P A 5 a P B hat is, the acceleration of the partirence is the same as that measured city relative to the first frame. r Figure 4.20 A particle located at P is described by two observers, one in the fixed frame of reference A and the other in the peed of ver has a e Earth. locity of bank. s a river will not end up W N vbr E you relau vre vbe W N E vbr v re a b 2 Page Figure 97, 4.21 erway (Example & Jewett 4.8) (a) A boat aims directly across a u vbe

5 Relative Motion Practice: Concepts Three motorboats are crossing a river. All have the same speed relative to the water. (a) ketch resultant vectors for each boat showing the speed and direction of the boats. Rank them from most to least for (b) the fastest ride. (c) the time to reach the opposite shore. 1 Figure and question from Hewitt, Conceptual Physics.

6 Relative Motion Practice uppose the river is 50 m wide, the motorboats move at 5 m/s relative to the water, the river has a current of 1 m/s, and that boat A makes an angle of 30 to the horizontal and boat C makes an angle of 60 to the horizontal as shown in the picture. (a) How long does it take each boat to cross? (b) How far downstream is boat B when it reaches the opposite shore? 1 Figure from Hewitt, Conceptual Physics.

7 Another Boat Question You are riding in a boat whose speed relative to the water is 6.1 m/s. The boat points at an angle of 25 upstream on a river flowing at 1.4 m/s. What is your velocity relative to the ground? 1 Figure from Walker, Physics.

8 Another Boat Question You are riding in a boat whose speed relative to the water is 6.1 m/s. The boat points at an angle of 25 upstream on a river flowing at 1.4 m/s. What is your velocity relative to the ground? ative to the water is 6.1 m/s. The boat points at an angle of 25 upstream our velocity relative to the ground? ketch:, and the y axis to boat relative to the he water relative to ts in the negative y v bw = 6.1 m/s v wg ction in which it is the boat will move of the boat we use g to the water (w), O 25 v bg v wg = 1.4 m/s x : s in the v! bg = v! bw + v! wg 1 Figurev! wg from= Walker, m/s2yn Physics.

9 Another Boat Question You are riding in a boat whose speed relative to the water is 6.1 m/s. The boat points at an angle of 25 upstream on a river flowing at 1.4 m/s. What is your velocity relative to the ground? ative to the water is 6.1 m/s. The boat points at an angle of 25 upstream our velocity relative to the ground? ketch:, and the y axis to boat relative to the he water relative to ts in the negative y v bw = 6.1 m/s v wg ction in which it is the boat will move of the boat we use g to the water (w), O 25 v bg v wg = 1.4 m/s x : Hypothesis: Less than 6.1 m/s, but more than = 4.7 m/s. The angle the velocity makes to the x-axis will be less than 25. v! bg = v! bw + v! wg s in the 1 Figurev! wg from= Walker, m/s2yn Physics.

10 m/s. Another The boat points Boatat Question an angle of 25 upstream the ground? y trategy: Vector addition. #» v bg = #» v bw + #» v wg v bw = 6.1 m/s v wg v bg O 25 v wg = 1.4 m/s x v! bw + v! wg 1 Figure from Walker, Physics.

11 3 6 RELATIVE MOTION 71 Another Boat Question m/s. The boat points at an angle of 25 upstream the ground? y v bw = 6.1 m/s v wg v bg O 25 v wg = 1.4 m/s x v! bw + v! wg m/s2yn 1 Figure from Walker, Physics.

12 Relative Motion Practice You are riding on a Jet ki at an angle of 35 upstream on a river flowing with a speed of 2.8 m/s. If your velocity relative to the ground is 9.5 m/s at an angle of 20.0 upstream, what is the speed of the Jet ki relative to the water? (Note: Angles are measured relative to the x axis, which points across the river.) 1 Walker, Physics, ch 3, problem 55.

13 Relative Motion Practice (Did yesterday) James. Walker, Physics, 4 th Edition You are v riding on a Jet ki at an angle of 35 upstream on a river 1 fw, x m/s tan tan 43 west of north flowing v with a speed 2.40 m/s fw, y of 2.8 m/s. If your velocity relative to the ground is 9.5 m/s at an angle of 20.0 upstream, what is the = x + y = speed of the ( Jet ki ) + relative ( to) = the water? θ = = = vfw vfw, vfw, 2.25 m/s 2.40 m/s 3.29 m/s er with respect to the ferry, then v would have to be shorter and point fw (Note: Angles are measured relative to the x axis, which points across the river.) ketch: r to that depicted in the figure at ski. he flow of the river, such that the et v = bw jet ski s velocity relative to the ground, and v = wg water s 3-8 to find the vector v bw, and then v + v v = v v bw wg bw bg wg ( 9.5 m/s) cos 20.0 xˆ + ( 9.5 m/s) sin 20.0 yˆ ( 8.9 m/s) xˆ + ( 3.2 m/s) yˆ 1 Walker, Physics, ch 3, problem 55.

14 Relative Motion Practice For the same river, suppose the Jet ki is moving at a speed of 12 m/s relative to the water. (a) At what angle must you point the Jet ki if your velocity relative to the ground is to be perpendicular to the shore of the river? (b) If you increase the speed of the Jet ki relative to the water, does the angle in part (a) increase, decrease, or stay the same? Explain. (Note: Angles are measured relative to the x axis, which points across the river.) 1 Walker, Physics, ch 3, problem 56.

15 ummary relative motion Homework Walker Physics: Ch 3, onward from page 76. Problems: 49, 57