OVERVIEW: This ball toss assignment has some of the basic components needed to model any falling object. In this scenario:(1) The object has an initial velocity (it is tossed upwards); (2) The object is subject gravity (an acceleration of approximately -9.81 m/sec2). (Note the negative sign.) To get the position of the ball, we must model the change in velocity over time and relate it to the height of the ball.

REVIEW KINEMATICS FROM PHYSICS

The motion of an object in free fall is modeled by: h= h0+ v0t + 1/2 at2h: vertical position(m)h0: initial height (m)v0: initial velocity (m/s) t: time(s) (the time that has elapsed between ball positions h0and h) a: acceleration, without drag it is just gravity (-9.81 m/s2) This equation accounts for the force of gravity but does NOT consider the drag associated with the friction of the air. In later tasks, our model will include considerations for drag. The drag will be a force in the opposite direction which is related to the density of the medium through which the object is moving. The drag force is different throughout the entire flight of the ball since the velocity is consistently changing. In preparation for later tasks, we should not simply use the above equation to model the height of a parachutist because the parachutist is certainly affected by drag. Taken alone, the equation above is not sophisticated enough capture drag (because acceleration depends on velocity and velocity depends on acceleration); but, we can use this equationas well see in later tasksif we choose small enough time steps and only model the objects position one step at a time.

NEW METHOD OF CALCULATION: TIME STEPPING Time stepping is characterized by the following structure: NEXT VALUE =CURRENT VALUE +CHANGE VALUE For the ball toss or the sky dive the 4 main components will be: Time, Height, Velocity, and Acceleration. With each of these components we can make simple assumptions and use computer programming to model more complex falling-object situations (like a sky dive). The main assumption is that for a small-time interval (dt) the velocity is constant. With this assumption, change in distance is simply constant velocity, v(I),multiplied by travel time, Ditmore explicitly, the next height equals the current height plus the change in height(note that the units of height are distance m (meters), so change has to be m/s * s.):height(i+1) = height(I) + velocity(I)*dt; Similar with velocity, where the next velocity equals the current velocity plus the change in velocityv(or gravity multiplied by time, m/s2* sin this case):velocity(i+1) = velocity(I) + g*dt; This problem and subsequent problems require time to be built using time stepping to ensure the time array matches your height, velocity, and in the future acceleration. Time would be: time(i+1) = time(I) + dt; PARACHUTE PROJECT TASK 1STEPS1.Initialize your code with the following parameters: TABLE 1: INITIAL VARIABLES

Variable Initial value g-9.81m/s2 to (initial time)0sTf (final time)10sN (number of steps)1000dt (time step)? (must find) Vo (initial velocity)30 m/sHo (initial height) 0m2.Run the time step simulation for the number of steps denoted in Table 1. 3.Plot the height and velocity as they change in the simulation. Remember to label your graphs appropriately.