A - A hummingbird flies 2.7 m along a straight path at a height of 5.3 m above the ground. Upon spotting a flower below, the hummingbird drops directly downward 1.8 m to hover in front of the flower. a) What is the magnitude of the hummingbird’s total displacement? Answer in units of m.
sqrt(2.7^2 + 5.3^2) is NOT CORRECT
B - How many degrees below the horizontal is this total displacement? Answer in units of ◦
moved down 1.8 not 5.3 meters
thanks, professor, I skipped over the height of the flower.
To find the magnitude of the hummingbird's total displacement, we need to find the straight distance from its starting point to its ending point. Since the hummingbird flies 2.7 meters along a straight path and then drops 1.8 meters vertically downward, we can use the Pythagorean theorem to calculate the magnitude of its total displacement.
First, we square the horizontal displacement (2.7 meters) and the vertical displacement (5.3 + 1.8 = 7.1 meters):
(2.7)^2 + (7.1)^2 = 7.29 + 50.41 = 57.70
Next, we take the square root of the sum to find the magnitude of the total displacement:
√(57.70) = 7.60
So, the magnitude of the hummingbird's total displacement is approximately 7.60 meters.
Now, to find the angle below the horizontal, we need to use trigonometric functions. The angle can be determined by taking the inverse tangent (arctan) of the vertical displacement (7.1 meters) divided by the horizontal displacement (2.7 meters).
θ = arctan(7.1/2.7)
Using a calculator, we find:
θ ≈ 70.43 degrees
Therefore, the hummingbird's total displacement is approximately 7.60 meters, and the angle below the horizontal is approximately 70.43 degrees.