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CBSE Class 11-science Answered

Derive equation of for a particle moving in a plane and show that motion can be resolved in two independent motion in mutually direction.
Asked by mohitsharma06474 | 12 Aug, 2019, 02:27: AM
answered-by-expert Expert Answer
Displacement in 2-D plane  begin mathsize 14px style S with rightwards arrow on top space equals space S subscript x space i with hat on top space plus space S subscript y space j with hat on top space end style
Velocity in 2D-plane    begin mathsize 14px style V with rightwards arrow on top space equals space V subscript x space i with hat on top space plus space V subscript y space j with hat on top space end style
Acceleration in 2D-plane   begin mathsize 14px style a with rightwards arrow on top space equals space a subscript x space i with hat on top space plus space a subscript y space j with hat on top space end style
where i and j are unit vectors along x-axis and y-axis of cartesian coordinate system.
 
For uniform accelerated motion we have 3 equations of motion in vector form
 
begin mathsize 14px style v with rightwards arrow on top space equals space u with rightwards arrow on top space plus space a with rightwards arrow on top space t space space................ left parenthesis 1 right parenthesis
S with rightwards arrow on top space equals space u with rightwards arrow on top t space plus space 1 half space a with rightwards arrow on top space t squared space space.............. left parenthesis 2 right parenthesis
v with rightwards arrow on top times v with rightwards arrow on top space equals space u with rightwards arrow on top times u with rightwards arrow on top space plus space 2 space a with rightwards arrow on top times S with rightwards arrow on top space space.......... left parenthesis 3 right parenthesis end style
 
If we choose a cartesian coordinate system, motion in any direction can be resolved in x-direction and y-direction.
 
Resolved form of equations (1), (2) and (3) are used to describe the motion individually in x and y directions.
 
Then resultant of resolved component will be considered to get net effect.
 
For example,  in x-direction, resolved form of eqn.(1) along x-direction, i.e., " vx = ux + ax t "
can be used to find the relation among initial velocity ux along x-direction, final velocity vx along y-direction,
acceleration ax along x-direction and time duration t
Answered by Thiyagarajan K | 12 Aug, 2019, 01:44: PM
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