How does the position vector change from 1-Dimension to 2-Dimensions? What about

Question

How does the position vector change from 1-Dimension to 2-Dimensions? What about the displacement vector? Explain. The big question l have is: How do we model the motion of an object moving in the x-direction AND y-direction over a time interval? Meaning, how has our model changed from 1D to 2D? How has the model stayed the same? Don't answer this question yet, use these situations to help answer this question: Situation A: l give you an initial velocity in the y-direction of a rock thrown straight upwards, on the surface of the earth write out how would you find the displacement after a time t? Situation B: I give you an initial velocity of a rock, launched at a specific angle, on the surface of the earth write out how would you calculate the displacement of the rock after a time t? Write out answers to: How are the procedures for answering the question in situation A and situation B the same? How are the procedures for answering the question in situation A and situation B different? Now write out an answer the overall question asked at the beginning of this problem X2-How has our model changed from 1D to 2D? How has the model stayed the same?

Explanation / Answer

X1:

in 1 dimension, it is assumed that the object is moving along / parallel to

one axis.

so the position of object at any point is measured along that axis and reported to be its position vector.

in 2- dimensions, the object is assumed to be moving in a plane

of two axes or parallel to plane of two axes so that its position

is represented by two coordinates and position vector as the vector

connecting origin to the point represented by those two coordinates.

example:

1 D motion:

let an object is moving along x axis.

then x=4 or x=5 or so on can be its position at any time and position vector will be

the vector connecting origin to that point.

2 D motion:

let an object is moving in xy plane.

then its position can be represented by (x,y)

and the vector connecting origin to this point is its position vector.

X2.

situation 1:

here the motion is confined to only y axis.

so you find out acceleration along y axis, initial velocity along y axis

and then displacement at any time t is given by

displacement=initial displacement+ initial velocity*time+0.5*acceleration*time^2

situation 2:

to calculate displacement, you need to calculate x coordinate and y coordinate at any time t

and then total displacement =vector sum of displacement along x axis and displacement along y axis

as presented in situation 1,

displacement along each axis can be found by finding their initial displacement,initial velocity

and acceleration along that axis.

answer to the questions :

Q1. what remains same in both situations?

ans: the procedure to calculate displacement along any axis remains same.

Q2. what changes in both situations?

ans: the final displacement claculation changes as in 2-D , displacement along both the

axes need to be added vectorically to find the final displacement.

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