A hummingbird flies 1.6 m along a straight

path at a height of 5.4 m above the ground. Upon spotting a flower below, the hummingbird drops directly downward 2.4 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. D^2 = X^2 + Y^2.

D^2 = (1.6)^2 + (-2.4)^2 = 8.32
D = 2.88 m.

B. tanA = Y/X = -2.4/1.6 = -1.5
A = -56.3o = 56.3o below the hor.

A.) The magnitude of the hummingbird's total displacement can be found using the Pythagorean theorem. We can see that the hummingbird flies 1.6 m horizontally and drops 2.4 m vertically. Therefore, the magnitude of the total displacement is the square root of (1.6^2 + 2.4^2).

Calculating that, we get √(1.6^2 + 2.4^2) = √(2.56 + 5.76) = √8.32 ≈ 2.887 m.

So, the magnitude of the hummingbird's total displacement is approximately 2.887 m.

B.) To find how many degrees below the horizontal the total displacement is, we can use trigonometry. The angle can be calculated using the inverse tangent function of the vertical displacement divided by the horizontal displacement.

The angle will be tan^(-1) (2.4 / 1.6) = tan^(-1) (1.5) ≈ 56.31°.

Therefore, the total displacement is approximately 56.31° below the horizontal.

To calculate the hummingbird's total displacement, we can use the Pythagorean theorem because the hummingbird flies along a straight path. The displacement in the horizontal direction will be equal to the distance it flew in the beginning minus the distance it dropped vertically.

A.) The horizontal displacement is 1.6 meters and the vertical displacement is 2.4 meters. Using the Pythagorean theorem, we can calculate the magnitude of the total displacement:

Total Displacement = √(horizontal displacement)^2 + (vertical displacement)^2
Total Displacement = √(1.6^2 + 2.4^2)

Simplifying this equation, we get:

Total Displacement = √(2.56 + 5.76)
Total Displacement = √(8.32)
Total Displacement ≈ 2.88 meters

Therefore, the magnitude of the hummingbird's total displacement is approximately 2.88 meters.

B.) To find the angle below the horizontal, we can use trigonometry. The angle θ can be calculated using the following equation:

θ = tan^(-1)(vertical displacement / horizontal displacement)

θ = tan^(-1)(2.4 / 1.6)

Calculating this equation gives us:

θ ≈ tan^(-1)(1.5)

Using a calculator, we find:

θ ≈ 56.31°

Therefore, the total displacement is approximately 2.88 meters and it is approximately 56.31° below the horizontal.

To find the magnitude of the hummingbird's total displacement, we can use the Pythagorean theorem.

First, let's consider the horizontal displacement. The hummingbird flies 1.6 m along a straight path at a height of 5.4 m. This horizontal displacement remains unchanged when the hummingbird drops vertically.

So, the horizontal displacement is 1.6 m.

Next, let's consider the vertical displacement. The hummingbird drops directly downward 2.4 m to hover in front of the flower.

So, the vertical displacement is -2.4 m (negative because it's downward).

Now, we can calculate the magnitude of total displacement. Using the Pythagorean theorem, we have:

Magnitude of displacement = sqrt(horizontal displacement^2 + vertical displacement^2)

Plugging in the values, we get:

Magnitude of displacement = sqrt((1.6^2) + (-2.4^2))
= sqrt(2.56 + 5.76)
= sqrt(8.32)
≈ 2.88 m

Therefore, the magnitude of the hummingbird's total displacement is approximately 2.88 m.

To find the angle below the horizontal, we can use trigonometry. We can use the inverse tangent function (arctan) to find the angle.

Angle = arctan(vertical displacement / horizontal displacement)

Plugging in the values, we get:

Angle = arctan(-2.4 / 1.6)
≈ -56.31 degrees

Therefore, the total displacement of the hummingbird is approximately 2.88 m with an angle of approximately -56.31 degrees below the horizontal.