Angela, Mary, and Tiff are all standing near the intersection of University and
ID: 3013917 • Letter: A
Question
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 14 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.)
(x, y) =
When does she reach this spot? (Round your answer to one decimal place.)
sec
Explanation / Answer
From the diagram,we can say that Tiff's coordinate is (50,120) and Angela's coordinate is (0,0)
The equation of line that is the distance between Angela and Tiff is y=2.4x
Here the slope is 2.4
Therefore the slope of perpendicular=-1/2.4
And Mary's coordinate is (0,50)
Therefore on using y=mx+b we get b=50
Therefore the required equation is y=(-1/2.4)x + 50
And to find the point of intersection we have to do
2.4x=(-1/2.4)x +50
x=17.7515
And when x=17.7515,y= 2.4*17.7515=42.6036
Therefore Angela's coordinate when she is near to Mary is (17.75,42.60)
And distance between Angela and this point is sqrt((0-17.75)2+(0-42.60)2)=46.15 feet
And she is running at a spped of 14 feet/sec
Therefore time taken to reach 46.15 feet=46.15/14=3.3 secs