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Motion II - PowerPoint PPT Presentation

Motion II. 2 and 3 dimensional motion. Components of Motion . Motion in 2 dimensions X component Y component Motion in 3 dimensions X component Y component Z component. Motion in x direction is independent of motion in y direction and z direction.

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Motion II

2 and 3 dimensional motion

• Motion in 2 dimensions

• X component

• Y component

• Motion in 3 dimensions

• X component

• Y component

• Z component

Motion in x direction is independent of motion in y direction and z direction.

Separate set of equations of motion for each direction.

Equations of Motion direction and z direction.

• ax= Fx/ m

• vx = vox + axt

• x = xo+ voxt + (1/2)axt2

• vx2 = vox2 + 2ax(x – xo)

• ay= Fy/ m

• vy = voy + ayt

• y = yo+ voyt + (1/2)ayt2

• vy2 = voy2 + 2ay(y – yo)

• a direction and z direction.z= Fz/ m

• vz = voz + axzt

• z = zo+ vozt+ (1/2)azt2

• vz2 = voz2 + 2az(z – zo)

Independence of x, , z motion direction and z direction.

• Motion in the x direction is independent of motion in the y or z directions.

• Motion in the y direction is independent of motion in the x or z directions

• Motion in the z direction is independent of motion in the x or y directions.

Nerf Gun Experiment direction and z direction.

• In class, a nerf gun was fired horizontally from a height of 3’10” and struck the ground at a distance of 16’10”.

• Calculate the muzzle velocity of the projectile.

• Calculate the time of flight of the projectile.

• Neglecting aerodynamic drag, the projectile leaves the muzzle with a velocity vo = vox.

• The projectile as it leaves the muzzle has no velocity in the y-direction, i.e. voy = 0.

• The only force on the projectile after it leaves the muzzle is the force of gravity.

• The acceleration in the y direction (up and down) is g = 32.2 ft/s2.

• In acceleration in the y direction is 32.2 ft/secthat time of 0.488 sec, the projectile travels

• 16.833 ft in the horizontal direction.

• vx = 16.833/0.488 = 34.49 ft/sec

• So the muzzle velocity is 34.49 ft/sec

Elevated Nerf Gun acceleration in the y direction is 32.2 ft/sec

• Consider the same nerf gun, but now elevated at an angle of ϴ⁰ to the horizontal.

• The muzzle velocity is vo

• The horizontal velocity vox = vocosϴ

• The vertical velocity is voy= vosinϴ

• vyvo

• vx

• v muzzle is gravity – in the y-direction.y2 = voy2 + 2ay(y – yo)

• voy = vosinϴ

• ay = - g

• vy2 = vo2sin2ϴ + (2)(-32.2)(y – yo)

• If ϴ = 30⁰ and vo = 28.0 ft/sec

• 0 = (28.0)2 (0.5)2 – 64.4 (y – yo)

• (y – yo) = 3.04 ft

• During that entire 0.87 sec, the projectile is moving in the x-direction at its initial speed.

• There is no force in the x-direction causing it to speed up or slow down.

• Its speed in the x- direction is (28)(0.866) ft/sec = 24.25 ft6/sec

• In 0.87 sec, the projectile travels (0.87)(24.25)

• = 21.1 feet in the x-direction before it impacts the ground!

Review x-direction at its initial speed.

• Motion in 2 dimensions

• X component

• Y component

• Motion in 3 dimensions

• X component

• Y component

• Z component

Motion in x direction is independent of motion in y direction and z direction.

Separate set of equations of motion for each direction.

Class Activity direction and z direction.

• Consider a rifle with a muzzle velocity of 3,000 ft/sec firing at ϴ⁰ to the horizontal.

• Calculate the range and time to impact as a function of ϴ.

• Create an excel worksheet and plot range vsϴ.

• At what value of ϴ would you get the maximum range? Analytically and graphically!