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Projectile Motion

Projectile Motion

If you throw a javelinWhat affects its flight?GravityHow hard you throw it (initial velocity)What angle you throw it atAir resistance (shape of javelin)Mass

Which one of these has no affect?

Lets take a look at how they affect flight!http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/ProjectileMotion/jarapplet.html

We call the arc of the javelin toss: Projectile MotionProjectiles travel along a curved trajectory

Projectile MotionA video introductionWhat is a Projectile?Projectile an object that moves along a 2-D curved trajectory- does not have any propulsion when in flightExamples: Football, baseball, tennis ball, etcBulletsSnow boarders in a half pipeCliff diversProjectile Motion Example # 1

What do you notice about these two projectiles?

Did you notice?The projectiles hit the ground at the same time regardless of horizontal velocityObject accelerates downwards (at 9.81 m/s2 acceleration due to gravity)Horizontal displacement stays constant throughout motion

Conclusions about Projectile motionThe horizontal component of a projectiles velocity is constant (no acceleration)Projectile experiences constant downwards acceleration (gravity)Horizontal and vertical motion of a projectile are independent of each other (except they have a common time)

Projectile Motion Example # 2

Important VariablesTime tVelocity vHeight dyDistance dXAcceleration aLaunch Angle -

Strategy to Solving Projectile Motion ProblemsAnalyze horizontal motion and vertical motion independentlySeparate the velocity vector into x- and y- componentsRemember: Time is common between themHorizontal motion:- Constant velocity (0 accel.) in the x direction- Equation : v = d/tVertical motion:- Constant acceleration - 9.8 m/s2 [down]- Use the accel. equations we used previously

Two Types of Problems: One Dimensional Problems (no horiz. Velocity)Case 1: Object dropped from restCase 2: Object thrown directly upwards

Two Dimensional Problems:Case 3: Rolled over an edgeCase 4: Shot at an angle

Lets analyze the four cases!For Two Dimensional Problems:Break the initial velocity into horizontal and vertical components (using the given angle and trigonometry)

vy

vx

Projectile Motion Example # 3

Example Question (Case 3)A tennis ball is rolled off a counter at 8 m/s, what will its position be after 3s?

Example Question (Case 4)A golfer strikes a golf ball on level ground. The ball leaves the ground with an initial velocity of 42 m/s [32o above the horizontal]. a) What will the balls position be after 4 s?b) What will be the maximum height attained?