Project 1
Part 1
The objective of this project is to accurately predict the trajectory of a solid object. In
this part of the project we will neglect the air resistance. Thus, the motion of a solid object
is described by
y 00 (t) = −g, x00 (t) = 0,
where (x(t), y(t)) are the coordinates of the center of mass. The object is launched with
initial velocity
x0 (0) = v0 cos(θ), y 0 (0) = v0 sin(θ)
and the initial position is given by x(0) = 0, y(0) = y0 .
We will use the data that was collected by P. Howard by firing sponge darts from a toy
gun. The time that takes for a dart fired straight up from a height 0.39 meters to hit ground
is 2.13 seconds.
1) Using this information compute v0 .
2) Determine the distance, d(θ), your object travels as a function θ, and compute the
angle that maximizes the distance. Take y0 = 0.18 meters. Plot this function on MATLAB
and compare it with an experimental data obtained with y0 = 0.18 and θ = 5, 10, 15, ..., 85
degrees. The data are given in a separate file along with M-file that will plot the distance
traveled in horizontal direction. Note that there are four sets of data due to the inaccuracies
in the experiment.
3) Plot a trajectory (x(t), y(t)) of the object at θ = 30 degrees.
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