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.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects