Question

Figure 3: Flight of an arrow without air resistance. When an arrow encounters no air resistance the laws of projectile motion from high-school physics apply. Using x for the horizontal distance traveled, f(x) for the height of the arrow when it is x units away, and \theta for the initial angle, we have this model for the trajectory of an arrow without air resistance: \begin{equation} f(x) = \tan\theta x - \frac{16}{200\cos\theta}x^2 \end{equation} When there is a drag on the arrow proportional to its velocity(k is the proportion factor), the height of the arrow is given by: \begin{equation} g(x) = \tan(\theta) x + \frac{200\cos\theta}{32} - \frac{32}{k} \log\left(\frac{200\cos\theta}{200\cos\theta - kx}\right) \end{equation} For both models, the range of flight is the time that y \ge 0. (When y \le 0, the definition of both g(x) and f(x) should be set to 0.) The range can be written as [0,b]. First, we investigate an arrow's flight without wind resistance. Exercise 6: 1. Let \theta = \frac{\pi}{4}. Look carefully at f(x), it is a quadratic polynomial in x. Rewrite f(x) so that the coefficients appear as (careful with the scientific notation) $f(x) = ax^2 + bx + c$ Now represent this polynomial in MATLAB, as in [a b c]. What are the values: Enter a short answer. 2. Use your previous answer and the roots function to find the range ([0,b]) of an arrow when shot at an angle of \frac{\pi}{4}. Specify the range in terms of its endpoint b Enter a number

          Figure 3: Flight of an arrow without air resistance.
When an arrow encounters no air resistance the laws of projectile motion from high-school physics apply. Using x for the horizontal distance traveled, f(x) for the height of the arrow
when it is x units away, and \theta for the initial angle, we have this model for the trajectory of an arrow without air resistance:
\begin{equation} 
f(x) = \tan\theta x - \frac{16}{200\cos\theta}x^2
\end{equation}
When there is a drag on the arrow proportional to its velocity(k is the proportion factor), the height of the arrow is given by:
\begin{equation} 
g(x) = \tan(\theta) x + \frac{200\cos\theta}{32} - \frac{32}{k} \log\left(\frac{200\cos\theta}{200\cos\theta - kx}\right)
\end{equation}
For both models, the range of flight is the time that y \ge 0. (When y \le 0, the definition of both g(x) and f(x) should be set to 0.) The range can be written as [0,b].
First, we investigate an arrow's flight without wind resistance.
Exercise 6:
1. Let \theta = \frac{\pi}{4}. Look carefully at f(x), it is a quadratic polynomial in x. Rewrite f(x) so that the coefficients appear as (careful with the scientific notation)
$f(x) = ax^2 + bx + c$
Now represent this polynomial in MATLAB, as in [a b c]. What are the values:
Enter a short answer.
2. Use your previous answer and the roots function to find the range ([0,b]) of an arrow when shot at an angle of \frac{\pi}{4}. Specify the range in terms of its endpoint b
Enter a number

Figure 3: Flight of an arrow without air resistance.
When an arrow encounters no air resistance the laws of projectile motion from high-school physics apply. Using x for the horizontal distance traveled, f(x) for the height of the arrow
when it is x units away, and θfor the initial angle, we have this model for the trajectory of an arrow without air resistance:

f(x) = tanθ x - (16)/(200cosθ)x^2

When there is a drag on the arrow proportional to its velocity(k is the proportion factor), the height of the arrow is given by:

g(x) = tan(θ) x + (200cosθ)/(32) - (32)/(k)log((200cosθ)/(200cosθ - kx))

For both models, the range of flight is the time that y ≥0. (When y ≤0, the definition of both g(x) and f(x) should be set to 0.) The range can be written as [0,b].
First, we investigate an arrow's flight without wind resistance.
Exercise 6:
1. Let θ= (π)/(4). Look carefully at f(x), it is a quadratic polynomial in x. Rewrite f(x) so that the coefficients appear as (careful with the scientific notation)
f(x) = ax^2 + bx + c
Now represent this polynomial in MATLAB, as in [a b c]. What are the values:
Enter a short answer.
2. Use your previous answer and the roots function to find the range ([0,b]) of an arrow when shot at an angle of (π)/(4). Specify the range in terms of its endpoint b
Enter a number

Added by Jennifer J.

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