22 Jan '10 03:45>6 edits
hello all, stuck on a problem looking for some insight
A particle travels along the path, y^2 = 4x with a constant speed of V = 4(m/s). determine the x, and y components of the particles velocity and acceleration when the particle is at x = 4(m)
im going to use prime notation for ease of formatting
heres where im at so far
a particles velocity is tangent to its path so I need to find the slope of the function at the given x
y^2 = 4x
2y*y'(x) = 4
y'(x) = 2/(y)
y'(4) = 1/2
from here I can find Vx,and Vy (the x-y components of the velocity respectivley)
from the right triangle (2,1,Sqrt(5))
@x=4......{y'(t) =Vy = ||V||*1/sqrt(5) = 4/sqrt(5)
..............{x'(t) = Vx = ||V||*2/sqrt(5) = 8/sqrt(5)
Now to find the components of the acceleration
y'(x) = 2/y
y'(t) = (2/y)(x'(t))
y"(t) = 2*[(-1/y^2)*(y'(t))*(x'(t)) + (1/y)(x"(t))]
here is where im stuck
1 equation 2 unknows and i'm having trouble coming up with another independent equation for either
y"(t) or x"(t)
does anyone see something about the acceleration that could help me out?
A particle travels along the path, y^2 = 4x with a constant speed of V = 4(m/s). determine the x, and y components of the particles velocity and acceleration when the particle is at x = 4(m)
im going to use prime notation for ease of formatting
heres where im at so far
a particles velocity is tangent to its path so I need to find the slope of the function at the given x
y^2 = 4x
2y*y'(x) = 4
y'(x) = 2/(y)
y'(4) = 1/2
from here I can find Vx,and Vy (the x-y components of the velocity respectivley)
from the right triangle (2,1,Sqrt(5))
@x=4......{y'(t) =Vy = ||V||*1/sqrt(5) = 4/sqrt(5)
..............{x'(t) = Vx = ||V||*2/sqrt(5) = 8/sqrt(5)
Now to find the components of the acceleration
y'(x) = 2/y
y'(t) = (2/y)(x'(t))
y"(t) = 2*[(-1/y^2)*(y'(t))*(x'(t)) + (1/y)(x"(t))]
here is where im stuck
1 equation 2 unknows and i'm having trouble coming up with another independent equation for either
y"(t) or x"(t)
does anyone see something about the acceleration that could help me out?