Question 157527: A robin is flying south for the winter at a rate of 40 mph when it runs into a hurricane, blowing due west at 100 mph. What is the new velocity of the robin?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A robin is flying south for the winter at a rate of 40 mph when it runs into a hurricane, blowing due west at 100 mph. What is the new velocity of the robin?
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40 mph is one leg and 100 mph the 2nd leg of a right triangle. It's a right triangle since south (180 degrees) is perpendicular to west (270 degs).
Use Pythagoras to find the speed, v^2 = 40^2 + 100^2
v^2 = 11600
v = sqrt(11600) = 107.7 mph
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The question was the "new velocity", not just speed. Speed is a scalar, velocity a vector that specifies speed and direction. Velocity is often said when the person means speed.
To find the ground track, note that the tangent of the angle between the heading of the robin (180 degs) and its 100 mph movement west (270 degs) is the arctan of 100/40, or arctan(2.5), for an angle of 68.2 degs.
So the robin is facing south, but moving over the ground at 180 + 68.2,
=~248 degrees, or WSW (west south west).
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