Projectile Motion 3 2 The Components of a

Projectile Motion

3 -2 The Components of a Vector Even though you know how far and in which direction the library is, you may not be able to walk there in a straight line:

3 -2 The Components of a Vector Can resolve vector into perpendicular components using a two-dimensional coordinate system:

3 -2 The Components of a Vector Length, angle, and components can be calculated from each other using trigonometry:

3 -2 The Components of a Vector Signs of vector components:

3 -3 Adding and Subtracting Vectors Adding vectors graphically: Place the tail of the second at the head of the first. The sum points from the tail of the first to the head of the last.

3 -6 Relative Motion The speed of the passenger with respect to the ground depends on the relative directions of the passenger’s and train’s speeds:

3 -6 Relative Motion This also works in two dimensions:

Vector Components y v 90° vy θ vx x SOH CAH TOA

Equations Of Motion • Velocity as a function of time vf = vi + at • Average Velocity vavg = (vf +vi) / 2 • Position as a function of time xf = xi + vit + ½ at 2 • Velocity in terms of Displacement vf 2 = vi 2 + 2 a(xf - xi)

• A geologist observes a volcano shoot a lava bomb and finds that it takes 4. 75 s for that lava bomb to go straight up and then back down to its original launch height. What is its initial speed? Then draw three graphs showing the position, velocity, and acceleration as a function of time.

What we know? • • • t = 4. 75 s a= -9. 8 m/s 2 xi = 0 xi = xf Vi = ? Which equation of motion do we use? • vf = vi + at • vavg = (vf +vi) / 2 • xf = xi + vit + ½ at 2 • vf 2 = vi 2 + 2 a(xf - xi)

x v t t a t

Question • A soccer ball is kicked at an angle of 35° from the ground. If the velocity of the ball is 20 m/s, compute the horizontal and vertical velocities of the ball at the instant of kick.

Answer

4 -3 Zero Launch Angle Launch angle: direction of initial velocity with respect to horizontal

• Gravity free

• Fast

• Slow

4 -5 Projectile Motion: Key Characteristics Range: the horizontal distance a projectile travels If the initial and final elevation are the same:

Range • Range = (vi 2/g) sin 2θ • What angle = maximum range? • When sin 2θ =1, so since sin 90 =1 • Θ = 45

Marble Catch Lab • Obj: Predict the landing spot of a projectile launched horizontally from an elevated platform. • Materials: incline, marble, stopwatch, meter stick • IMPORTANT: The marble must never leave the table when taking data. Only when you are ready to shoot for your grade will the ball be allowed to land on the floor.

Procedure • 1. Roll the steel ball down the ramp several times, recording the necessary data to determine the average speed at which it will be launched horizontally off the table. 2. Take any measurements needed to calculate the time of free fall for the projectile to hit the floor. 3. Using the launch velocity and calculated time, predict by calculation the landing spot of your projectile. Measure this calculated distance from a spot on the floor directly below the edge of the table. Place the target sheet at this position, making sure the ball’s velocity vector is aligned with the center of the paper. 4. Call over the physics teacher before firing the projectile for your grade. The target sheet gives your grade.