Ready, Aim, Fire I got a fever… And the only prescription is… More potato cannon!

What do we do?  Define the goal or the problem  Brain dump, literature search  Organize the research  Assess progress toward goals periodically

What’s our goal?  To hit a ‘castle wall’ of defined size

What’s the easy way to do this?  Get reaaaaally close!  Is it the best approach?  Consequences of being too close?

Restated goal?  To hit the ‘castle wall’ while being at a maximum distance away considering the capabilities of the potato cannon

Brain dump… What do you know? What do you need to know?

Summary of work so far  Used actual data to verify value of accel due to gravity  Used freefall equations to analyze potato fired straight up in air  Various activities to analyze projectile motion –Ball and chair –Bottle caps launched off table

How can we verify the bottle cap activity?  Do they really hit the ground at the same time? Or not?  We need an experiment with data!

To prepare for the lab and the project…  Need to figure out what equations apply –In the horizontal direction –In the vertical direction

Treat motion in x, y directions independently  Horizontal direction –assume constant velocity, v x = constant – x = v x t Vertical direction - freefall, accel due to gravity - y = ½ a t 2 + v i t + y i - v = at + v i

Summary of concepts so far –Without air drag, projectile motion can be analyzed as a combination of  Constant velocity in the x or horiz direction Using specific c.v. equation for position  Accel motion, i.e. freefall in the y, vert dir Using specific equations for position and velocity  Although motions are independent, time is common

Simplified for horiz launched projectiles…  X direction x = v x t Y direction Y direction y = 5t 2 v = 10 t

Get ready for ‘ball in the cup’ challenge!  Predict the speed of the ball as it rolls along and off the table  Predict where the ball lands  Place ball in predicted spot  We need to practice prediction, e.g math, skills for horizontal launches

Now let’s look at angled launch not just horizontally launched…  What do they know at PhET that we don’t know?

Investigating projectile motion  Simulation on Colorado website –Investigated variables that may affect our goal of max range or horiz direction –Is the simulation a good way to analyze our goal? –What do the simulation’s programmers know that we do or do not know?

What have we learned from the Colorado simulation?  Effect of different variables such as: –Angle –Initial velocity –Initial height of cannon –Air drag Which of these variables are you going to include in your cannon project?

What types of situations can we analyze right now?  Shot straight up?  Shot horizontally?  Shot at an angle?  What do we still need to know?

Calculations we can do so far…  Vertical launch  Horizontal launch  Non-horizontal but only if we are given horiz and vertical velocities

Our equations are strictly x direction, strictly y direction  How can we figure out the x and y initial velocities of a potato launched with some initial velocity at an angle?  Velocity in x dir v x = ? Initial vel in y dir v y i = ?

Heeeey, SOHCAHTOA!  What’s your vector, Victor? –PhET computer activity Assume that Vel. of potato as it leaves the cannon V = 25 m/s Then v x = V [cos (θ angle)] v y i = V [sin (θ angle)] SOHCAHTOA

Time to get serious….  What progress have you made?  Are you ready to do calculations?  Have you determined your initial conditions and told me?  Started writing report? –Discussion of variables  Controllable vs not controllable  Can be included in calc’s vs lack info to be able to include in calc’s

How to predict, calculate range?  Identify x i, y i, v x, v y i, y f  Define up as +, down as -  Use general eqns Horiz dirX = v x t Vert dirY = -5t 2 + v y i t + y i v = -10t + v y i SOLVE FOR X but HAVE TO FIND t

Practice, practice, practice!  Marble launcher activity –Use all knowledge to date  to determine launch velocity –Photogate or other technique?  Set angle  Predict range  Test…can you hit the target?  Same skills required to predict range for potato cannon launch!!