Chapter 11 Relative Velocity

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Leon Taylor
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1 Chapter 11 Relatie Velocity 11 Relatie Velocity Vector add like ector, not like nuber. Except in that ery pecial cae in which the ector you are adding lie along one and the ae line, you can t jut add the agnitude of the ector. Iagine that you hae a dart gun with a uzzle elocity 1 of 45 ph. Further iagine that you are on a bu traeling along a traight highway at 55 ph and that you point the gun o that the barrel i leel and pointing directly forward, toward the front of the bu. Auing no recoil, a it leae the uzzle of the gun, how fat i the dart traeling relatie to the road? That right! 100 ph. The dart i already traeling forward at 55 ph relatie to the road jut becaue it i on a bu that i oing at 55 ph relatie to the road. Add to that the elocity of 45 ph that it acquire a a reult of the firing of the gun and you get the total elocity of the dart relatie to the road. Thi proble i an exaple of a cla of ector addition proble that coe under the heading of Relatie Velocity. It i a particularly eay ector addition proble becaue both elocity ector are in the ae direction. The only challenge i the ector addition diagra, ince the reultant i right on top of the other two. We diplace it to one ide a little bit in the diagra below o that you can ee all the ector. Defining to be the elocity of the bu relatie to the road, to be the elocity of the dart relatie to the bu, and DB to be the elocity of the dart relatie to the road; we hae DB FORWARD The ector addition proble thi illutrate i + DB If we define the forward direction to be the poitie direction, DB FORWARD Poitie Direction then, becaue the ector we are adding are both in the ae direction, we are indeed dealing with that ery pecial cae in which the agnitude of the reultant i jut the u of the agnitude of the ector we are adding: 1 The uzzle elocity of any gun i the elocity, relatie to the gun, with which the bullet, BB, or dart exit the barrel of the gun. The barrel exit, the opening at the front end of the gun, i called the uzzle of the gun, hence the nae, uzzle elocity. 6

Iagine that you hae a dart gun with a uzzle elocity 1 of 45 ph.

2 Chapter 11 Relatie Velocity + DB + DB 55 ph + 45 ph 100 ph 100 ph in the direction in which the bu i traeling You already know all the concept you need to know to ole relatie elocity proble (you know what elocity i and you know how to do ector addition) o the bet we can do here i to proide you with oe ore worked exaple. We e jut addreed the eaiet kind of relatie elocity proble, the kind in which all the elocitie are in one and the ae direction. The econd eaiet kind i the kind in which the two elocitie to be added are in oppoite direction. Exaple 11-1 A bu i traeling along a traight highway at a contant 55 ph. A peron itting at ret on the bu fire a dart gun that ha a uzzle elocity of 45 ph traight backward, (toward the back of the bu). Find the elocity of the dart, relatie to the road, a it leae the gun. Again defining: to be the elocity of the bu relatie to the road, to be the elocity of the dart relatie to the bu, and DB to be the elocity of the dart relatie to the road, and defining the forward direction to be the poitie direction; we hae DB + DB DB 55 ph 45 ph 10 ph FORWARD Poitie Direction 10 ph in the direction in which the bu i traeling 63

We e jut addreed the eaiet kind of relatie elocity proble, the kind in which all the elocitie are in one and the ae direction.

3 Chapter 11 Relatie Velocity It would be odd looking at that dart fro the ide of the road. Relatie to you it would till be oing in the direction that the bu i traeling, tail firt, at 10 ph. The next eaiet kind of ector addition proble i the kind in which the ector to be added are at right angle to each other. Let conider a relatie elocity proble inoling that kind of ector addition proble. Exaple 11- A boy itting in a car that i traeling due north at 65 ph ai a BB gun (a gun which ue a copreed ga to fire a all etal or platic ball called a BB), with a uzzle elocity of 185 ph, due eat, and pull the trigger. Recoil (the backward oeent of the gun reulting fro the firing of the gun) i negligible. In what copa direction doe the BB go? Defining to be the elocity of the car relatie to the road, CR to be the elocity of the BB relatie to the car, and BC to be the elocity of the BB relatie to the road; we hae NORTH BC 185 ph EAST CR 65 ph θ tanθ θ tan 1 BC CR BC CR 185 ph θ tan 1 65 ph θ 70.6 The BB trael in the direction for which the copa heading i

Let conider a relatie elocity proble inoling that kind of ector addition proble.

4 Chapter 11 Relatie Velocity Exaple 11-3 A boat i traeling acro a rier that flow due eat at 8.50 /. The copa heading of the boat i Relatie to the water, the boat i traeling traight forward (in the direction in which the boat i pointing) at 11. /. How fat and which way i the boat oing relatie to the bank of the rier? Okay, here we hae a ituation in which the boat i being carried downtrea by the oeent of the water at the ae tie that it i oing relatie to the water. Note the gien inforation ean that if the water wa dead till, the boat would be going 11. / at 15.0 Eat of North. The water, howeer, i not till. Defining to be the elocity of the water relatie to the ground, WG to be the elocity of the boat relatie to the water, and to be the elocity of the boat relatie to the ground; we hae NORTH φ / EAST θ W G 8.50 / Soling thi proble i jut a atter of following the ector addition recipe. Firt we define +x to be eatward and +y to be northward. Then we draw the ector addition diagra for. WG Breaking it up into coponent i triial ince it lie along the x-axi: 65

How fat and which way i the boat oing relatie to the bank of the rier?

5 Chapter 11 Relatie Velocity y, North W G 8.50 / x, Eat By inpection: WGx 8.50 / W Gy 0 Breaking doe inole a little bit of work: y, North x inθ x y x inθ φ / x 11. in(15.0 o ) x. 899 coθ y x, Eat y y y o 11. co(15. 0 ) coθ Now we add the x coponent to get the x-coponent of the reultant 66

inθ φ 15.0 11. / x 11. in(15.0 o ) x. 899 coθ y x, Eat y y y o 11. co(15.

6 Chapter 11 Relatie Velocity WGx + x and we add the y coponent to get the y-coponent of the reultant: y WGy + y y y Now we hae both coponent of the elocity of the boat relatie to the ground. We need to draw the ector coponent diagra for to deterine the direction and agnitude of the elocity of the boat relatie to the ground. y, North y θ x x, Eat We then ue the Pythagorean Theore to get the agnitude of the elocity of the boat relatie to the ground, 67

8 Now we hae both coponent of the elocity of the boat relatie to the ground.

7 Chapter 11 Relatie Velocity + y ( /) + (10. 8 /) / and the definition of the tangent to deterine the direction of : tanθ θ tan θ tan 1 1 θ y o y / / Hence, 15.6 / at 43.8 North of Eat. 68

64 / and the definition of the tangent to deterine the

Description: Conceptual questions about projectile motion and some easy calculations. (uses applets)

Description: Conceptual questions about projectile motion and some easy calculations. (uses applets) Week 3: Chapter 3 [ Edit ] Overview Suary View Diagnotic View Print View with Anwer Week 3: Chapter 3 Due: 11:59p on Sunday, February 8, 2015 To undertand how point are awarded, read the Grading Policy