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A particle projected from origin moves in x-y plane with a velocity v= 3i+ 6j where I and j are the unit vector along x and y axis. Find the equation of path followed by the particle

A particle projected from origin moves in x-y plane with a velocity v= 3i+ 6j where I and j are the unit vector along x and y axis. Find the equation of path followed by the particle

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
 You want the equation of the trajectory of the particle, only for its motion along the y axis. 
Here, the velocity along the y axis is dependent on x. 
So, we first find x for any given time t. 
Using the second equation of motion, 
s = ut + 1/2(a * t^2) 
s = displacement, u = initial velocity, t = time, a = acceleration. 
So, taking the displacement along x axis to be x, 
x = 3t + 1/2(0 * t^2) 
So, x=3t 
Now, you get the component of velocity along the y axis in terms of t in which 
v (along y) = 6(3t) j = 18t j 
The next part involves calculus. 
To find the acceleration, differentiate v with respect to t and you get 
a = 18 j 
So, you can find the displacement along the y axis ( take it as y) using the second equation again 
y = ut + 1/2(a * t^2) 
At t = 0 the initial velocity u will be 0 
Therefore, y = 1/2 * a * t^2 
And as a = 18 
y = 9 * t^2
 

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