Angela Mary and Tiff are all standing near the intersection

Angela, Mary, and Tiff are all standing near the intersection of University and 42nd streets. Mary and Tiff do not move, but Angela runs toward Tiff at 12 ft/sec along a straight line, as pictured. Assume the roads are 50 feet wide and Tiff is 70 feet north of the nearest corner.? Where is Angela located when she is closest to Mary? (Let Angela\'s initial location be the origin. Round your answers to two decimal places.) When does she reach this spot? (Round your answer to one decimal place.)

Tiff Maryl \'L 42 nd St. Angela University Way iverS1

Solution

Solution:

Angela\'s intial location is (0,0) and as the roads are 50\' wide then Mary\'s location is (0,50) and Tiff\' is at (50,110).

The line joining Angela to Tiff has the equation y = 2.2x [Since - use slope intercept form and Tiff\'s coordinates ;

110 = 2.2 * 50]

Angela is closest to Mary when a perpendicular from the line y = 2.2x passes though the point where Mary is

standing.

The product of the slopes of perpendicular lines is -1

The slope of the perpendicular line is thus -1/2.2

In slope-intercept form the equation of the perpendicular line is y = mx + c

Substituting -1/2.2 for m and using Mary\'s coordinates this gives, 50 = -0/2.2 + c.

Thus c = 50 and the line equation becomes y = -x/2.2 + 50.

At the point where the two lines intercept we can 2.2x = -x/2.2 + 50

Then, 4.84x = -x + 110 : 5.84x = 110 : x = 18.8356

By Using the initial line equation,

the corresponding value of y is : y = 2.2x = 2.2*18.8356 = 41.4384

Use Pythagoras to determine the distance (L) travelled by Angela to get to this point.

L² = 18.8356² + 41.4384² = 354.78045 + 1717.1374

L = 45.518

As Angela is running at 12 fps then she covers this distance in 45.518/12 = 3.79 seconds.