Aparticle moves along the parabolic path given by y^2=4x in such a way that when it is at the point (1,-2), its horizontal velocity (in the direction of the x-axis) is 3ft/s. what is its vertical velocity (in the direction of the y-axis) at this instant? show work and answer in the comments!

The particle's position as a function of time is parameterized by the ordered pair of functions , with



If we differentiate both sides of this equation with respect to time , we have



where the derivatives of and represent change in horizontal and vertical position, respectively, over time. In other words, these are the particle's horizontal/vertical velocities.

We're told that the horizontal velocity at a certain point in time - namely, when the particle's position is (1, -2) - is 3 ft/s, which is to say that at some time , we have



In other words, under the given conditions, the particle has a downward vertical velocity of 3 ft/s.

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