Question

Margot is walking in a straight line from a point 20 feet due east of a statue in a park toward a point 12 feet due north of the statue. She walks at a constant speed of 5 feet per second. (a) Write parametric equations for Margot's position t seconds after she starts walking.

Answer 1

Answer:

a) $x = 20\,ft - \left(12\,\frac{ft}s}\cdot \cos 59.036^{\textdegree} \right)\cdot t$, $y = 0\,ft +\left(12\,\frac{ft}{s}\cdot \sin 59.036^{\textdegree}\right)\cdot t$

Step-by-step explanation:

Let consider +x and +y the north and east directions. Given that Margot travels at constant speed, the formula is:

$v = \frac{s}{t}$

Where:

$t$ - Time, in seconds.

$s$ - Travelled distance, in meters.

The traveled distance is:

$s = v\cdot t$

a) The parametric equations are described below:

$x = 20\,ft - \left(12\,\frac{ft}s}\cdot \cos 59.036^{\textdegree} \right)\cdot t$

$y = 0\,ft +\left(12\,\frac{ft}{s}\cdot \sin 59.036^{\textdegree}\right)\cdot t$