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 ◦.
https://www.jiskha.com/display.cgi?id=1508283496
change the 2.7 to 1.8....
It's still incorrect.
ok, now reading it like a lawyer, it dropped down 1.8
displacement= sqrt(1.8^2 + 2.7^2)
angle= arctan(1.8/2.7)
To find the magnitude of the hummingbird's total displacement, we can use the Pythagorean theorem. The total displacement is the vector sum of the horizontal displacement (2.7 m) and the vertical displacement (1.8 m).
Let's calculate it step by step:
1. Determine the magnitude of the horizontal displacement.
The horizontal displacement is given as 2.7 m.
2. Determine the magnitude of the vertical displacement.
The vertical displacement is given as 1.8 m.
3. Use the Pythagorean theorem to find the magnitude of the total displacement.
The Pythagorean theorem states that the square of the hypotenuse (total displacement) is equal to the sum of the squares of the two legs (horizontal and vertical displacements). In equation form, it is written as:
(total displacement)^2 = (horizontal displacement)^2 + (vertical displacement)^2
Substituting the given values, we have:
(total displacement)^2 = (2.7 m)^2 + (1.8 m)^2
Calculating the right-hand side of the equation:
(total displacement)^2 = 7.29 m^2 + 3.24 m^2 = 10.53 m^2
Taking the square root of both sides to solve for the total displacement:
total displacement = √(10.53 m^2)
Rounding off to the appropriate number of significant figures, the magnitude of the hummingbird's total displacement is approximately 3.25 m.
To determine the angle below the horizontal of the total displacement, we can use trigonometry. The angle can be found using the tangent function as:
angle = arctan(vertical displacement / horizontal displacement)
Substituting the given values:
angle = arctan(1.8 m / 2.7 m)
Calculating the right-hand side of the equation:
angle = arctan(0.67)
Using a calculator or reference table, we find that the angle is approximately 33.69 degrees below the horizontal.
Therefore, the magnitude of the hummingbird's total displacement is approximately 3.25 m, and it is approximately 33.69 degrees below the horizontal.