A hummingbird flies 2.4 m along a straight path at a height of 3.5 m above the ground. Upon spotting a flower below, the hummingbird drops. . .directly downward 1.7 m to hover in front of the...

A hummingbird flies 2.4 m along a straight path at a height of 3.5 m above the ground. Upon spotting a flower below, the hummingbird drops. . .

directly downward 1.7 m to hover in front of the flower. What's the magnitude of the hummingbird's total displacement? & How many degrees below the horizontal is this total displacement?

Expert Answers
ndnordic eNotes educator| Certified Educator

To solve problems of this type, construct a right triangle starting at the origin.  Go 2.4 m east, then 1.7 m south. Draw a line from the origin to the end of the line you drew south.  That is the hypotenuse of the right triangle.

To find the length of the hypotenuse use the Pythagorean Theorem. To find the angle use the inverse tan function.

Length = square root of (2.4^2 + 1.7^2) = 2.94 m.

Angle:  tan^-1(1.7/2.4) = 35.3 degrees south of east.

So the hummingbird is hovering 2.94 m from the starting point at an angle of 35.4 degrees south of east.

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