After a vigorous soccer match, Tina and Michael decide to have a glass of their

Question

After a vigorous soccer match, Tina and Michael decide to have a glass of their favorite refreshment. They each run in a straight line along the indicated paths at a speed of 10 ft/sec.

Write parametric equations for the motion of Tina and Michael individually after t seconds. (Round all numerical values to four decimal places as needed.)

Find when Tina and Michael are closest to one another. (Round your answer to four decimal places.)

s

Find where Tina and Michael are closest to one another. (Round your answers to three decimal places.)

Compute this minimum distance. (Round your answer to one decimal place.)
ft

Explanation / Answer

The distance between them can be calculated using the distance formula for Cartesian coordinates:
D = sqrt((x2-x1)^2 + (y2-y1)^2) which is nothing more than the Pythagorean theorem using x2-x1 and y2-y1 as the legs of the right triangle.
For your problem, the coordinates could be labeled xT,yT and xM,yM.This will give a formula
D = sqrt((xT - XM)^2 + (yT - yM)^2). If you substitute the parametric formulas for each of these coordinate points, you will have a distance formula in terms of t.
Take the first derivative of this and set it equal to zero. Solve for t and you will find the time when they are closest to each other. Put this time back into the distance formula and you will have the actual distance.

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