In biology, a vector is a disease-carrying organism, such as a mosquito. One such disease, West Nile Virus, is spread primarily by migratory birds. The figure below shows the spread of the Virus.

Question

West Nile Virus was first detected in New York in 1999. Two years later, the virus had spread to Miami, a distance of 1,100 miles at a direction of 7.00° west of south from New York. In 2002, the virus was found in Minneapolis, 1,500 miles at a direction 37.0° west of north from Miami. Finally, the virus arrived in San Diego in 2004, a distance of 1,550 miles at a direction 25.0° south of west.

(a) What is the net displacement (in mi) of the virus from 1999 to 2004? (Give the direction in degrees south of west, rounded to at least three significant figures.)

magnitude:

direction:

(b)

What is the average speed (in mi/h) of the spread of the virus from New York to San Diego during this time?

Speed:

Answer 1

This is a problem of decomposing 3 vectors into their x (positive East) and y (positive North) components and then finding the resultant vector.

New York - Miami x = 1100 * sin (7) = -134.1 (i.e. West)

y = 1100 * cos (7) = -1092 (i.e. South)

Miami - Minnesota x = 1500 * sin (37) = -902.7 (West)

y = 1500 * cos (37) = 1198 (north)

Minnesota - San Diego x = 1550 cos(25) = -1405 (West)

y = 1550 sin (25) = -655.1 (South)

So x_total = -2442 miles

y_total = -549.1 miles

Solve hypotenuse 2503 = sqrt(2442² + 549²) miles

The angle tan (Θ) = 549.1/2442)

Θ = 12.67 deg

Resultant vector is 2503 miles and 12.67 deg south of West

Average speed 500 miles/day or about 21 mph