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A meteorologist tracks the movement of a thunderstorm with Doppler radar. At 8:0

ID: 1531051 • Letter: A

Question

A meteorologist tracks the movement of a thunderstorm with Doppler radar. At 8:00 PM, the storm was 55 minortheast of her station. At 11:00 PM, the storm is at 75 mi north.   What is the direction of the average velocity of the storm?

What is the magnitude of the average velocity of the storm?

A student bikes to school by traveling first dN = 0.800 miles north, then dW = 0.300 miles west, and finally dS = 0.200 miles south.  Take the north direction as the positive y direction and east as positive x. The origin is still where the student starts biking. Let d N be the displacement vector corresponding to the first leg of the student's trip. Express d N in component form.

Explanation / Answer


(1) Find the position vectors

A = 55cos45 i + 55sin45 j

= 38.89 i + 38.89 j

B = 75 j

Displacement d = B - A

= -38.89 i + 36.10 j

direction

tan tita = (36.10/-38.89)
  
= -42.87degree

= -42.87 + 180 (to get into QIII)

= 137.13 degree from +x axis.

mag d = (38.89 + 36.10) mi = 75 mi

mag V = mag d / time

= 75 mi / 3 h = 25 mi/h

(2) Student bikes to school by traveling first dN = 0.800 miles north

Corresponding vector (V1)= 0 i + 0.8 j

student then bikes to school by traveling dW = 0.300 miles west

Corresponding Vector (V2) = -0.3 i + V1

= -0.3 i + (0 i + 0.8 j)

= -0.3 i + 0.8 j

student then bikes to school by traveling dS = 0.200 miles south

Corresponding Vector (V3) = -0.2 j + V2
  
= -0.2 j + ( -0.3 i + 0.8 j)

= -0.3 i + 0.6 j

  
dN = -0.3 i + 0.6 j