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an initial velocity v in the x-direction and v in the y-direction satisfies the
0, x
0, y
following parametric equations:
x = v t and y = − 1 gt + v t
2
0, x 0, y
2
where t is time and the origin of the axis was chosen to correspond to the
position of the particle at t = 0 and g = 9.8 ms –2
a. By eliminating the time t, show that the projectile trajectory y(x) is
a parabola.
b. Noting that the components of the initial velocity can be written
as function of the projectile initial speed and its angle of inclination:

v = v sin(φ) and v = v cos(φ)
0
0, x
0, y
0
show that, for a given initial speed, the maximum range for the
projectile is achieved when the inclination angle of the initial veloc-
ity is 45°.
c. Plot the range for a fixed inclination angle as a function of the initial
speed.

3.4 Examples with Polynomial Functions

As pointed out in the Supplement, a polynomial function is an expression of
the form:

px() = a x + a x n−1 +…+ a x + a (3.9)
n
n n−1 1 0
th
where a ≠ 0 for an n -degree polynomial. In MATLAB, we can represent the
n
polynomial function as an array:
p = [ a a … a ] (3.10)
nn−1 0
Example 3.1
You are given the array of coefficients of the polynomial. Write a function M-
file for this polynomial using array operations. Let p = [132103]:

Solution:

function y=polfct(x)
p=[1 3 2 1 0 3];

© 2001 by CRC Press LLC