Relative motion (Translating axes)

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Valentine Banks
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1 Relative motion (Tanslating axes) Paticle to be studied This topic Moving obseve (Refeence) Fome study Obseve (no motion) bsolute motion Relative motion If motion of the efeence is known, absolute motion of the paticle can also be found

2 Relative motion (2) = a paticle to be studied B = a (moving) obseve whose x-y axis is attached to Moving axes Motion of measued using X-Y axis is called the absolute motion Fixed axes Motion of measued by the obseve at B is called the elative motion of with espect to B Motion of /B Obseve B Note xes attached to the eath suface ae usually assumed to be fixed

3 Relative position Hee only the case whee the x-y is not otating is consideed. (only tanslating) Fixed axes Moving axes If the obseve at B use the x-y coodinate system to descibe the position vecto of we have xiˆ / B = + yj ˆ î and ĵ ae the unit vectos along x and y axes (x, y) is the coodinate of measued in x-y fame Note: Othe coodinate systems can also be used

4 bsolute and elative motion = B + / B Moving axes B / B : absolute position vecto of : absolute position vecto of B : elative position vecto of with espect to B Fixed axes & & & = B + / B Velocity v = vb + v/ B cceleation & & + & = a + a = B / B a B / B

5 bsolute and elative motion (2) Fo ectangula coodinate xiˆ / B = + yj ˆ Fixed axes Moving axes v ˆ ˆ / B= & / B= xi & + yj & a = && = && xiˆ+ && yj ˆ / B / B v ˆ ˆ = vb + v/ B = vb + xi & + yj & a = a + a = a + && xiˆ+ && yj ˆ B / B B Similaly any coodinate system may be used fo the absolute motion

6 Choice of obseve Paticle can also be used as the oigin of the efeence coodinate Fixed axes Moving axes = + v = v + v a = a + a B B/ B B/ B B/ It is seen that = / B B/ v = v / B B/ a = a / B B/

7 Sample poblem 2/12 Passenges in the jet tanspot flying east at a speed of 800 km/h obseve a second jet plane B that passes unde the tanspot in hoizontal flight. lthough the nose of B is pointed in the 45 notheast diection, plane B appeas to the passenges in to be moving away fom the tanspot at the 60 angle as shown. Detemine the tue velocity of B.

8 Sample poblem 2/13 Ca is acceleating in the diection of its motion at the ate of 1.2 m/s 2. Ca B is ounding a cuve of 150-m adius at a constant speed of 54 km/h. Detemine the velocity and acceleation which ca B appeas to have to an obseve in ca if ca has eached a speed of 72 km/h fo the positions epesented.

9 Sample 3 (2/195) dop of wate falls with no initial speed fom point of a highway ovepass. fte dopping 6 m, it stikes the windshield at point B of a ca which is taveling at a speed of 100 km/h on the hoizontal oad. If the windshield is inclined 50 fom the vetical as shown, detemine the angle θ elative to the nomal n to the windshield at which the wate dop stikes.

Sample 4 (2/201) iplane is flying noth with a constant hoizontal velocity of 500 km/h. iplane B is flying southwest at the same altitude with a velocity of 500 km/h.

10 Sample 4 (2/201) iplane is flying noth with a constant hoizontal velocity of 500 km/h. iplane B is flying southwest at the same altitude with a velocity of 500 km/h. Fom the fame of efeence of detemine the magnitude v of the appaent o elative velocity of B. lso find the magnitude of the appaent velocity v n with which B appeas to be moving sideways o nomal to its centeline. Would the esults be diffeent if the two aiplanes wee flying at diffeent but constant altitude.

Sample 5 (2/203) fte stating fom the position maked with the x, a football eceive B uns the slant-in patten shown, making a cut at P and theeafte unning with a constant speed v b = 7 m/s in the

11 Sample 5 (2/203) fte stating fom the position maked with the x, a football eceive B uns the slant-in patten shown, making a cut at P and theeafte unning with a constant speed v b = 7 m/s in the diection shown. The quateback eleases the ball with a hoizontal velocity of 30 m/s at the instant the eceive passes point P. Detemine the angle α at which the quateback must thow the ball, and the velocity of the ball elative to the eceive when the ball is caught. Neglect any vetical motion of the ball.

Sample 6 (2/204) The aicaft with ada detection equipment is flying hoizontally at an altitude of 12 km and is inceasing its speed at the ate of 1.2 m/s each second.

12 Sample 6 (2/204) The aicaft with ada detection equipment is flying hoizontally at an altitude of 12 km and is inceasing its speed at the ate of 1.2 m/s each second. Its ada locks onto an aicaft B flying in the same diection and in the same vetical plane at an altitude of 18 km. If has a speed of 1000 km/h at the instant when θ = 30, detemine the values of & & and & θ at the same instant if B has a constant speed of 1500 km/h.

13 Sample 7 (2/205) batte hits the ball with an initial velocity of v 0 = 30 m/s diectly towad fielde B at an angle of 30 to the hoizontal; the initial position of the ball is 0.9 m above gound level. Fielde B equies 0.25 s to judge whee the ball should be caught and begins moving to that position with constant speed. Because of geat expeience, fielde B chooses his unning speed so that he aives at the catch position simultaneously with the ball. The catch position is the field location with the ball altitude 2.1 m. Detemine the velocity of the ball elative to the fielde at the instant the catch is made.

Kinematics in 2-D (II)

Kinematics in 2-D (II) Unifom cicula motion Tangential and adial components of Relative velocity and acceleation a Seway and Jewett 4.4 to 4.6 Pactice Poblems: Chapte 4, Objective Questions 5, 11 Chapte