A fly lands on one wall of a room. The lower-left corner of the wall is selected as the origin of a two-dimensional Car- tesian coordinate system. If the fly is located at the point having coordinates (2.00, 1.00) m, (a) how far is it from the origin? (b) What is its location in polar coordinates?
Answers
Answer:
a) The fly is 2.24 m from the origin.
b) In polar coordinates, the position of the fly is (2.24 m, 26.7°).
Explanation:
Hi there!
The position vector of the fly is r = (2.00, 1.00)m. The distance from that point to the origin is the magnitude of the vector "r" (see figure).
a) Notice in the attached figure that the distance from the origin to the point where the fly is located is the hypotenuse of the triangle formed by r, the x-component of r (2.00 m) and the y-component ( 1.00 m). Then:
r² = (2.00 m)² + (1.00 m)²
r² = 5.00 m²
r = 2.24 m
The fly is 2.24 m from the origin.
b) To find the angle θ (see figure) we can use trigonometry:
cos θ = adjacent / hypotenuse
cos θ = 2.00 m / √5 m
θ = 26.7°
The same will be obtained if we use sin θ:
sin θ = opposite / hypotenuse
sin θ = 1.00 m / √5 m
θ = 26.7°
In polar coordinates, the position of the fly is (2.24 m, 26.7°).
Related Questions
1. Two charges Q1( + 2.00 μC) and Q2( + 2.00 μC) are placed along the x-axis at x = 3.00 cm and x=-3 cm. Consider a charge Q3 of charge +4.00 μC and mass 10.0 mg moving along the y-axis. If Q3 starts from rest at y = 2.00 cm, what is its speed when it reaches y = 4.00 cm?
The unit of electric potential or electromotive force is the
An electron has a velocity of 3.2 x 10^6 m/s. What is its’ momentum? (b) What is its’ wavelength? (c) What other objects/materials have this space/size? (d) Assuming that we can measure the velocity to an accuracy of 10%. Use the Heisenberg uncertainty principle to calculate the uncertainty in the position.
4 A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When it has made 10 rev determine its angular velocity.]
Answers
Displacement means when you move something from its original position. Let's say you want to sit on a chair. You move the chair from where it was originally placed. That's displacement.
Answers
Answer:
The magnetic field at the center of the solenoid is approximately 0.0117 T
Explanation:
Given;
length of the solenoid, L = 15 cm = 0.15 m
number of turns of the solenoid, N = 350 turns
current in the solenoid, I = 4.0 A
The magnetic field at the center of the solenoid is given by;
Therefore, the magnetic field at the center of the solenoid is approximately 0.0117 T.
Answers
Answer:
The speed must a ball be thrown vertically from ground level to rise to a maximum height is 28.35 m/s.
Explanation:
Given;
maximum vertical height of the throw, H = 41 m
Apply the following kinematic equation;
V² = U² + 2gH
where;
V is the final speed with which the ball will rise to a maximum height
U is the initial speed of the ball = 0
g is acceleration due to gravity = 0
V² = U² + 2gH
V² = 0² + 2gH
V² = 2gH
V = √2gH
V = √(2 x 9.8 x 41)
V = 28.35 m/s
Therefore, the speed must a ball be thrown vertically from ground level to rise to a maximum height is 28.35 m/s.
Answers
Answer:
wavelength of the standing wave will be equal to 30 cm
Explanation:
We have given length of the guitar string L = 60 cm
Mass per unit length
Frequency is given f = 660 Hz
We have to find the wavelength of the standing wave
Length of the string will be 2 times of the wavelength of the wave
So
So wavelength of the standing wave will be equal to 30 cm
Answers
the light bulb converts the electricity to light and heat.
in a fluorescent bulb, it is different, but the electricity is again converted to light, very little heat, though.
So, for the first blank electric, and the second blank the better answer is light.
Answers
All of that is fascinating information. Thank you for sharing.