Friday July 3, 2009

Research Project Studying the Projectile Motion


You will create a MS Word file and include all your results and observations there. This time, I expect your files to include:
  • A Title

  • Your name, program, date, location, and name of your professor

  • One sentence Statement of the Problem or purpose of the project

  • One sentence or two on your approach (methodology)

  • Your results, including observations below each

  • Conclusions

  • Note: Due to lack of time, I haven't asked you to provide theoretical background.

    The projectile motion is a two-dimensional motion where the projectile moves in x (distance) and in y (height) directions.  In this motion the projectile is usually sent of from its initial location (x0 and y0) with an initial speed (v0) at an initial angle (angle0).

    Assuming our initial velocity is v0 = 40 (m/s) and the initial angle is angle = 35 degree. The initial horizontal and vertical speeds are computed using:

     

    InitialHorizontalSpeed = v0 * cos(angle)

    InitialVerticalSpeed = v0 * sin(angle)

     

    On Earth gravitational constant g = -9.8 (m/s^2).

     

    We want to create 4 different plots to:

    Note that horizontal speed will never change and it is always the same as InitialHorizontalVelocity. The above values are computed as following (note three are time-dependent):

     

    horizontal distanceInitialHorizontalSpeed*time
    height =  (1/2)*g*time^2 + InitialVerticalSpeed * time + initialHeight
    verticalSpeed = g*time + InitialVerticalSpeed


    Please note that in Excel you have to type angle by pi/180 to convert to Radian. you will type angle*PI()/180. For example:
    =v0*COS(angle*PI( )/180)

     

    Also note that the horizontal speed will stay the same as the initial one:

    horizontalSpeedInitialHorizontalSpeed

    Once again note that the last one is always constant because it is not time-dependent. Thus, we need to compute these values at some time instances.  We will use the total time that the projectile is traveling before it comes to stop and will create equally spaced time instances between 0 to some TMAX.  TMAX is computed as:


    TMAX = -v0*sin(angle0)/g

     

    So you need to start the time from 0 and end it at TMAX. Use an Excel spreadsheet to solve this problem. Please use cell naming for angle, v0, Initial height, and g.

      

    What will happen to the graph if we repeat the same experiment on planets:

    moon: g = -1.63333 m/s2

    Mars: g = -3.326667 m/s2

    Europa (moon of Jupiter): g = -1.61 m/s2

     

    Create all the graphs for these cases and make your observations. E-mail me one report containing your results and observations.

     

    Remember, your goal is to investigate:

    The effect of initial velocity on the projectile motion (you can try 6 different cases)

    The effect of initial angle on the projectile motion (you can try 6 different cases)

    The effect of g on the projectile motion (you already have 4 to use and may add 2 more)

    Anything else that you might have thought about and I forgot to say J ?

     

    Now one challenging problem. Suppose the initial speed of the projectile, v0, is 100 m/s. What would be an initial angle if we want the projectile to reach a maximum height of 50 m? You need to solve this using gold seed.

    hint: Maximum height will happen at TMAX.

     Make sure you have saved your file before you leave the lab.