Projectile motion y=f(x) type ,

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A particle moves along the curve y=e^(2x) with a constant velocity of 4 ft/s. To find the x and y components of the velocity when y=5 ft, the derivative dy/dx is calculated as 2e^(2x). The confusion arises in solving for the components dx/dt and dy/dt, which can be derived from the equation [(dx/dt)^2 + (dy/dt)^2]^(1/2) = 4 ft/s. By substituting dy/dt into the velocity equation, one can solve for dx/dt and subsequently find dy/dt. Understanding these relationships is crucial for solving the problem correctly.
th3plan
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This is for my dynamics class, but anywaya. A particle moves along a curve y=e2x such that its velocity has a constant magnitude of v=4ft/s. Determine the x and y components of the velocity when y =5ft ?

Im confused on this. So when i plug 5 into the equation is get .804 ft. Now that's the movement in the x direction. then i differentiate and get a tangent line to the curve. dy/dx=2e2x . Now I am confused. What i do. Can someone please explain me this. Its bugging me like crazy!
 
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A particle moves along a curve y=e^2x
Take derivative with respect to time t.
It is given that [(dx/dt)^2 + (dy/dt)]^2]1/2 = 4 ft/s
Solve for dx/dt and dy/dt.
 
Yes. I got that but how do i solve for the dy/dt and dx/dt that's what i don't get .
 
dy/dt = 2e^2X*dx/dt = 2y*dx/dt.
Substitute dy/dt in the equation and solve for dx/dt.
 

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