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.
B - How many degrees below the horizontal is this total displacement? Answer in units of ◦
a. sqrt(2.7^2+5.3^2)
b. what is arc tan 2.7/5.3
To find the magnitude of the hummingbird's total displacement, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this scenario, we can consider the hummingbird's initial 2.7 m trajectory along a straight path as one side of the triangle, and the 1.8 m vertical drop as the other side. The total displacement will be the hypotenuse.
Using the Pythagorean theorem:
Total displacement^2 = (2.7 m)^2 + (1.8 m)^2
Total displacement^2 = 7.29 m^2 + 3.24 m^2
Total displacement^2 = 10.53 m^2
Total displacement = √10.53 m^2
Total displacement ≈ 3.24 m
Therefore, the magnitude of the hummingbird's total displacement is approximately 3.24 m.
To determine the angle below the horizontal of this total displacement, we can use trigonometry. Let's call this angle θ.
Sin θ = Opposite / Hypotenuse
Sin θ = 1.8 m / 3.24 m
θ = sin^(-1)(1.8 m / 3.24 m)
θ ≈ 32.3°
Therefore, the total displacement is approximately 32.3° below the horizontal.
To find the total displacement of the hummingbird, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the horizontal displacement is 2.7 m and the vertical displacement is 1.8 m.
a) To find the magnitude of the total displacement, you can use the Pythagorean theorem:
Total Displacement = √(horizontal displacement^2 + vertical displacement^2)
= √(2.7^2 + 1.8^2)
Evaluating this equation will give you the magnitude of the hummingbird's total displacement in units of meters.
b) To find the angle below the horizontal, you can use basic trigonometry. The angle can be found using the inverse tangent function:
Angle below horizontal = atan(vertical displacement / horizontal displacement)
Evaluating this equation will give you the angle in units of degrees.