query 192

course phy201

19.2019. `query 19

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Question: `qQuery class notes #20

Explain how we calculate the components of a vector given its magnitude and its angle with the positive x axis.

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Your solution:

We would calculate the x component of the magnitude by x=magnitudecos(angle) and the y component by y=magnitude sin(angle)

confidence rating #$&*

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Given Solution:

`a** STUDENT RESPONSE:

x component of the vector = magnitude * cos of the angle

y component of the vector = magnitude * sin of the angle

To get the magnitude and angle from components:

angle = arctan( y component / x component ); if the x component is less than 0 than we add 180 deg to the solution

To get the magnitude we take the `sqrt of ( x component^2 + y component^2) **

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Self-critique (if necessary):

ok I understand that magnitude = sqrt(x^2 + Y^2)

and angle or direction = tan-1(y/x)

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Self-critique rating #$&*3

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Question: `qExplain what we mean when we say that the effect of a force is completely equivalent to the effect of two forces equal to its components.

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Your solution:

if forces from x component and y compenten are added then you have the total effect of the force

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Given Solution:

`a** If one person pulls with the given force F in the given direction the effect is identical to what would happen if two people pulled, one in the x direction with force Fx and the other in the y direction with force Fy. **

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Self-critique (if necessary):

ok, i understand

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Self-critique rating #$&*3

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Question: `qExplain how we can calculate the magnitude and direction of the velocity of a projectile at a given point.

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Your solution:

We calulate the magnitude by using the pythegorean therum, sqrt(x^2 + y^2)

we calculate the direction of a velocity by tan-1(y/x)

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Given Solution:

`a** Using initial conditions and the equations of motion we can determine the x and y velocities vx and vy at a given point, using the usual procedures for projectiles.

The magnitude of the velocity is sqrt(vx^2 + vy^2) and the angle with the pos x axis is arctan(vy / vx), plus 180 deg if x is negative. **

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Self-critique (if necessary):

ok, so if the total of x is negative we add 180 if it is positve we add 360....I rmeber this now.

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Question: `qExplain how we can calculate the initial velocities of a projectile in the horizontal and vertical directions given the magnitude and direction of the initial velocity.

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Your solution:

if we know the magnitude of the initital velocity and direction of velocity ce can calculate the final velocity and from there find the time in the vertical direction. Horizontally we multiply the velocity by the time from the vertical to find the direction in the horizotnally

confidence rating #$&*

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Given Solution:

`a** Initial vel in the x direction is v cos(theta), where v and theta are the magnitude and the angle with respect to the positive x axis.

Initial vel in the y direction is v sin(theta). **

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Self-critique (if necessary):

ok,

so this was

x=v cos(theta)

y=v sin (theta)

????????????????????????????????????this says that there are the magnitude and the angle with respect to the positvie x aixs, I am not quite clear on this ar ethey added together??????????????????????????????????????????????????????????????????????????????

Check the expanded explanation below:

If an object is thrown straight up in the

air, its initial velocity is all in the vertical direction.  Its angle as

measured from the horizontal x axis is 90 degrees. It has no horizontal

velocity; the horizontal component of its velocity is zero. In this case our

calculations would verify the obvious:

cos(90 deg) = 0, so the x component of

the velocity is v_x = v cos(90 deg) = v * 0 = 0.

sin(90 deg) = 1, so the y component of

the velocity is v_y = v sin(90 deg) = v * 1 = v.

If an object is thrown in the horizontal

direction, its angle with the horizontal is 0 degrees.  Its velocity is

wholly in the horizontal direction.  The vertical component of its velocity

is zero.  Our calculations again verify this:

cos(0 deg) = 0, so the x component of

this velocity is v_x = v cos(0 deg) = v * 0 = 0.

sin(0 deg) = 1, so the y component of

this velocity is v_y = v sin(0 deg) = v * 1 = v.

Now if an object is thrown at some nonzero

angle with horizontal, as it typically the case, the magnitudes of its velocity

components are less than the magnitude of its velocity. 

For example an object thrown at angle 45

degrees, halfway between the direction of the x axis and that of the y axis, has

equal x and y components.  Our calculation verifies this

cos(45 deg) = .71, approx., so the x

component of this velocity is v_x = v cos(45 deg) = v * .71 = .71 v.

sin(45 deg) = .71, so the y component

of this velocity is v_y = v sin(45 deg) = v * .71 = .71 v.

An object thrown at 30 degrees, closer to

the direction of the x axis that to that of the y axis, has a velocity component

in the x direction which is greater than that in the y direction.  Our

calculation will verify this:

cos(30 deg) = .87, approx., so the x

component of this velocity is v_x = v cos(30 deg) = v * .87 = .87 v.

sin(30 deg) = .50, so the y component

of this velocity is v_y = v sin(30 deg) = v * .50 = .50 v.

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