Trajectory/Projectile motion



Trajectory/Projectile Motion Notes

Objectives:

“To understand the experimental and theoretical basis for describing motion as the superposition of two independent motions: (1) a body falling in the vertical direction, and (2) a body moving in the horizontal direction with no forces” (from Priscilla W. Laws, Workshop Physics. (Units 1-7) 1997.)

• To learn to describe positions, velocities, and accelerations using vectors.

• “Measure the velocity of a ball using two photogates and computer software for timing.

• Apply concepts from two-dimensional kinematics to predict the impact point of a ball in projectile motion.

• Take into account trial-to-trial variations in the velocity of measurement when calculations the impact point. “ (from Vernier 3rd Edition “Physics with Computers”, Experiment 8).

Overview:

The independent horizontal and vertical motion of an object causes a trajectory, or curved path, that forms a parabola. An object launched in earth’s gravitational field has the force of gravity acting in the vertical direction. Breaking the initial velocity into components, equations can be derived to solve for height or range of the projectile.

Trajectory/Projectile motion:

*Curved path is the result of two independent motions, a horizontal motion with uniform velocity and a vertical motion with uniform acceleration due to gravity. Motions are independent of each other. A projected ball will fall at the same rate of a dropped ball because the initial velocity is zero.

• There is an initial force and then gravity takes over.

• Note: at 45o hang-time=3.90s, range=74.5m, max height=18.6m

Useful equations:

Object launched horizontally

x= vxt

y= vyt + 1/2 gt2

t2=2y/g vy is 0

Object Not launched horizontally

*Must find the x and y components of initial velocity.

vx=vi cos θ

vy=vi sin θ

y= vyt + 1/2 gt2

t= -2vy/g y is 0

R = vxt

Ymax= vyt + 1/2 gt2 where t = 1/2 total time

y=H= vy2 –vi2 / 2

Note: Four assumptions are made when using these equations.

1. Air resistance can be ignored.

2. Curvature of earth can be ignored.

3. Gravity is considered to be constant.

4. The projectile has remained in the same vertical plane throughout its flight.

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