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2-Dimensional Motion - Projectiles. Now it starts to get more interesting (and don’t get freaked out by the equations and subscripts). Projectiles – What path do they follow?. http://www.us-inauguration-day-2009.com/human_cannonball.jpg. Projectiles follow parabolic paths. - PowerPoint PPT Presentation

### Transcript of 2-Dimensional Motion - Projectiles

2-Dimensional Motion - Projectiles

2-Dimensional Motion - ProjectilesNow it starts to get more interesting(and dont get freaked out by the equations and subscripts)Projectiles What path do they follow?

Most important thingto remember is that horizontal and verticalmotion are independentof one another.From now on,Horizontal = X directionVertical = Y directionLets look at the horizontal and vertical components individuallyWhich way does gravity point? DOWN!!!So, there is no gravity in the horizontal direction (x-direction)There is only gravity in the vertical direction (y-direction)So, in general, there is no acceleration in the horizontal direction (x-direction)Take a moment to let that sink in.This is where parabolic motion comes from. Why? Lets find out

What is the X-component of motion?Same as missing acceleration case for one-dimensional motion.X = V0TBut since we have 2 dimensions, we want to distinguish further between X and Y, soX = V0xTV0 = V naught = same thing as V initialThis is how the book writes it, so I dont want you to get confusedNow lets look at the Y-directionY direction has gravitySo, with no initial vertical speed, the position in the y-direction follows the free fall equation:Y = gt2However, there will be cases where we have an initial vertical speedY = V0yt+ ayt2 = V0yt + gt2 , where g = 9.8m/s2So, lets bring it togetherX stuffY stuff_______________X = horiz positionY = vert positionAx = accel in x-dirAy = accel in y-dirVx = velocity in x-dirVy = velocity in y-dirV0x = Init veloc in x-dirV0y = Init veloc in y-dirVfx = final veloc in x-dirVfy = final veloc in y-dirT = timeT = time

All the 1-D equations you know and love work in 2D!Just use subscripts!When once we hadNow we havev = atvx = axt, vx = v0x + axtx = at2x = axt2 , x = v0x t+ axt2 vf2 = vi2 + 2axvfx2 = vix2 + 2axx

And the same for the Y-directionJust use subscripts!When once we hadNow we havev = atvy = ayt, vy = v0y + ayty = at2y = ayt2 , y = v0y t+ ayt2 vf2 = vi2 + 2ayvfy2 = viy2 + 2ayxAnd remember that nine times out of ten, the acceleration in the y-direction (ay) = g = 9.8m/s2

So then why is projectile motion parabolic?Because of the interaction between X and Y components of motionEven though they are independent, the way in which they work together yields parabolic motionWhen there is acceleration in the y-direction (gravity) and NO acceleration in the x-direction, you have equation of the form x = f(t) and y = f(t2)x = v0x t and y = v0y t+ ayt2 Now, Lets look at some projectiles

http://media.photobucket.com/image/parabolic%20motion/Finer_Kitchens/Marilyn_CakeBalls/scan0008.jpgLets look at the velocity vectors what do you notice?

http://www.phys.ttu.edu/~rirlc/Lecture6.htmlExamine the two different components of the velocity X vs. Y

http://www.phys.ttu.edu/~rirlc/Lecture6.htmlFirst, note the launch angle 0The initial horizontal (X) component of V is given by Vcos()The initial vertical (Y) component of V is given by Vsin()

Examine the two different components of the velocity X vs. Y

http://www.phys.ttu.edu/~rirlc/Lecture6.htmlNow note that the vertical (Y) component of motion changesHorizontal (X) component stays the sameBecause Y component changes, Velocity vector changes both direction and magnitude during flight

Now lets look at some animationsFor motorcycle and archery fun, lets go to

http://www.mhhe.com/physsci/physical/giambattista/proj/projectile.html