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Anettt [7]
3 years ago
6

A vector A has components Ax = −4.00 m and Ay = 3.50 m. Find the magnitude (in m) and the direction (in degrees counterclockwise

from the +x-axis) of the vector.
Physics
1 answer:
8_murik_8 [283]3 years ago
4 0

Answer:

Part (i) the magnitude of the vector is 5.315 m

Part (ii) the direction of the vector is 138.8⁰

Explanation:

Given;

y-component Ay = 3.50 m

x -component Ax = -4.00 m

Vector representation = (-4i + 3.5j)

Part (i) the magnitude of the vector

Magnitude of the vector = √(-4)² +(3.5)²

Magnitude of the vector = √28.25

                                          = 5.315 m

Part (ii) the direction (in degrees counterclockwise from the +x-axis) of the vector.

If we make a rough sketch of this vector, the direction of this vector lies in second quadrant.

That is; 90 < θ < 180

Let's solve for θ

tan θ = y/x

tan θ = 3.5/-4

tan θ = - 0.875

θ = tan⁻¹ (-0.875)

θ = - 41.2⁰

Since θ lies in the second quadrant,

θ = - 41.2⁰ = 180 - 41.2 = 138.8⁰

The direction of the vector is 138.8⁰

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Dante is leading a parade across the main street in front of city hall. Starting at city hall, he marches the parade 4 blocks ea
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Answer:

The correct option is A)

Displacement: 6.71 m, Direction: 63.4 degrees north of east

Explanation:

Given that Dante is leading a parade across the main street in front of city hall.

Let, Initial location of parade is 0i+0j

One block of city is one units on the XY- graph

Statement 1: Parade marches the parade 4 blocks east, then 3 blocks south

New location of parade is 4i-3j

Statement 2: The parade marches 1 block west and 9 blocks north and finally stops.

Final location of parade is (4i-3j)+(-1i+9j)=3i+6j

Displacement is given by

Displacement = (Final destination)-(Initial destination)

Displacement = (3i+6j)-(0i+0j)=3i+6j

Thus,

Magnitude of displacement = \sqrt{3^{2}+6^{2}}

                                              = 6.71 m

Direction of displacement =  tan^{-1}(\frac{Y}{X} )

                                           =  tan^{-1}(\frac{6}{3} )

                                           = 63.43 NE

Therefore, the correct option is A) Displacement: 6.71 m, Direction: 63.4 degrees north of east

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antsy andy tries to push his 6kg desk away from him and finds that it takes him 12 N of force to start the desk from rest and 8
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Answer:

static coefficient = 0,203 & kinetic coefficient = 0,14

Explanation:

There are two (2) conditions, when the desk is about to move and when the desk is moving. In the attachements you can see the two free body diagram for each condition.

In the first condition, there is no movement and the force is 12 N, in the image we can see the total forces are equal to 0 and by the definition of the friction force we can get the static friction coefficient.

In the second condition there is movement in the direction of the force which is equal to 8 N, again by the definition of the friction force we can get the kinetic friction coefficient. Since the desk is moving with constant velocity there is not acceleration.

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