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.
How many degrees below the horizontal is this total displacement? Answer in units of ◦.
How would you go about the first part and how would the second part be completed?
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draw the triangle, verify the distances.
To find the magnitude of the hummingbird's total displacement, we can use the Pythagorean theorem as the motion forms a right-angled triangle. The horizontal displacement is 2.7 m, and the vertical displacement is 1.8 m.
Using the Pythagorean theorem, we can calculate the magnitude of the total displacement:
Total displacement = √(horizontal displacement² + vertical displacement²)
Total displacement = √(2.7² + 1.8²)
Total displacement = √(7.29 + 3.24)
Total displacement = √10.53
Total displacement ≈ 3.25 m (rounded to two decimal places)
Now, to find the angle below the horizontal, we can use trigonometry. The angle can be found using the inverse tangent function. Let's call this angle θ.
θ = tan^(-1)(vertical displacement / horizontal displacement)
θ = tan^(-1)(1.8 / 2.7)
θ ≈ tan^(-1)(0.6667)
θ ≈ 33.7 degrees (rounded to one decimal place)
Therefore, the magnitude of the hummingbird's total displacement is approximately 3.25 m, and the total displacement is approximately 33.7 degrees below the horizontal.
To find the magnitude of the hummingbird's total displacement, we can use the Pythagorean theorem. The total displacement is the straight-line distance from the initial position to the final position.
To solve for the magnitude of displacement (d), we can use the formula:
d = √(dx^2 + dy^2)
Where dx is the horizontal displacement and dy is the vertical displacement.
In this case, dx is the initial distance of 2.7 m and the final displacement of 0 m (since the bird ends up in front of the flower at the same horizontal position). dy is the vertical displacement of -1.8 m, since the bird drops down.
Now, let's calculate the magnitude of displacement:
d = √(2.7^2 + (-1.8)^2)
= √(7.29 + 3.24)
= √10.53
≈ 3.25 m
So, the magnitude of the hummingbird's total displacement is approximately 3.25 m.
Moving on to the second part, we need to find the angle below the horizontal that the total displacement makes. We can use trigonometry to solve this.
To find the angle (θ), we can use the formula:
θ = tan^(-1)(dy / dx)
where dy is the vertical displacement (-1.8 m) and dx is the horizontal displacement (2.7 m).
Now, let's calculate the angle:
θ = tan^(-1)(-1.8 / 2.7)
≈ tan^(-1)(-0.67)
≈ -33.69 degrees
Since the angle below the horizontal is negative, we can convert it to a positive angle.
θ = 360 degrees - |θ|
θ = 360 degrees - |-33.69|
θ ≈ 360 degrees - 33.69 degrees
θ ≈ 326.31 degrees
Therefore, the total displacement is approximately 326.31 degrees below the horizontal.