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Consider the motion of a particle in 2-dimensions given the Lagrangian:
where, λ>0. The initial conditions are y (0) =0, x (0) = 40 meters,
What is the value of x(t) - y(t) at t = 10 sec in meters?
where, λ>0. The initial conditions are y (0) =0, x (0) = 40 meters,
What is the value of x(t) - y(t) at t = 10 sec in meters?
- a)80
- b)40
- c)20
- d)10
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Consider the motion of a particle in 2-dimensions given the Lagrangian...
We are given with 
Now we use the Euler langrange equation which says:
Putting the expression for L in this equation we get:
Similarly, we get:
Now these two equations have
in common.
Hence equating both equation we get:
Integrating it once we get:
where c is some constant.
Putting the condition that
we get:
Now we have:
Integrating it once again we get:
where c1 is some constant of integration.
Now putting the conditions:
y (0) = 0, x(0) = 40 meters, we get:
40−0=c1
Now our equation becomes:
x(t)−y(t)=40.
Now we use the Euler langrange equation which says:
Putting the expression for L in this equation we get:
Similarly, we get:
Now these two equations have
in common.Hence equating both equation we get:
Integrating it once we get:
where c is some constant.Putting the condition that
we get:
Now we have:
Integrating it once again we get:
where c1 is some constant of integration.Now putting the conditions:
y (0) = 0, x(0) = 40 meters, we get:
40−0=c1
Now our equation becomes:
x(t)−y(t)=40.
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Consider the motion of a particle in 2-dimensions given the Lagrangian:where,λ>0.The initial conditions are y (0) =0, x (0) = 40meters,What is the value of x(t) - y(t) at t = 10sec in meters?a)80b)40c)20d)10Correct answer is option 'B'. Can you explain this answer?
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