Projectile Motion with force of air resistance

[hallowon]

Homework Statement

In my physics class, we are launching a base ball of mass 0.14273kg 40.0m at the target point. Part of the assignment involves presenting the data obtained by our groups, and all the necesarry efficiency calculation. The other part where it is tricky is that, we have to code a computer program to solve for air resistance, and use this to calculate the initial velocity of the ball.

Most of our marks come from how much the ball deviates from the target, and how we communicate using our calculations.

Homework Equations

programming language actionscript 3
Fair= Kv^2
component method
Fnetx= Fairx
Fnety= Fg+Fairy

we are launching at 45 degrees angle

The Attempt at a Solution

For what I know the vertical component of the air resistance is in the same vector direction as gravity on the way up and opposite of gravity on the way down.

To find the accurate measurement, i have to use a looping statement to solve for the new velocity at each set interval.

I stop the loop when vertical displacement is 0 - not really b/c the slingshot is not starting from the ground rather about 1m up the ground.

 

[jbsteele]

//For the calculation of air resistance //declare all variables var Vxi = 0; // initial velocity in x direction var Vyi = 0; // initial velocity in y direction var Vi = 0; // initial velocity var m = 0.14273; // mass of the ball var g = 9.81; // gravitational acceleration var K = 0.47; // coefficient of drag var t = 0; // time var dt = 0.1; // time step var vx = Vxi; // current velocity in x direction var vy = Vyi; // current velocity in y direction var v = Vi; // current velocity var x = 0; // displacement in x direction var y = 0; // displacement in y direction //calculate the velocity at each time step while (y >= 0) { Fairx = K*v*vx; Fairy = K*v*vy; Fnetx = Fairx; Fnety = Fg+Fairy; vx = vx + Fnetx/m*dt; vy = vy + Fnety/m*dt; x = x + vx*dt; y = y + vy*dt; t = t + dt;}//calculate the initial velocity Vi = sqrt(vx^2 + vy^2); //output initial velocity trace("The initial velocity of the ball is " + Vi + " m/s");

 

[kerimek]

I would like to commend you on your thorough approach to this assignment. Projectile motion with air resistance is a complex topic, and it is impressive that you are using a computer program to solve for the initial velocity and accurately measure the ball's deviation from the target.

Your equations and approach seem sound, and I would suggest using a numerical integration method such as Euler's method or the Runge-Kutta method to solve for the new velocity at each interval. This will provide a more precise calculation of the ball's trajectory.

Additionally, I would recommend considering other factors that may affect the ball's motion, such as the angle of launch and the coefficient of air resistance. These can also be incorporated into your program to provide a more comprehensive analysis.

Overall, it seems like you have a solid understanding of projectile motion and air resistance, and I am confident that your program and calculations will accurately represent the ball's trajectory and lead to a successful presentation and assignment.