- #1

- 100

- 5

## Homework Statement

(Translating from a Polish high school textbook, so if anything is unclear please let me know).

An object moves on a trajectory described by the parabola ##y=\frac{1}{2\lambda}x^2## such that the ##x## component of its velocity is constant and equal to ##v_0##. The ##\lambda## parameter, which is in units of length, is constant. At time ##t=0## the object was located at ##(x_0, y_0) = (0,0)##.

Show how the following depend on

*time*:

a) The ##x## and ##y## coordinates of the velocity vector.

b) The ##x## and ##y## coordinates of the tangential acceleration vector.

## Homework Equations

None

## The Attempt at a Solution

For part (a), I took advantage of the fact that ##v_0## in the ##x## direction is constant and rewrote the parabola equation as:

$$y=\frac{1}{2\lambda}(tv_0)^2$$

Differentiating, I get that the change in ##y## with respect to time = ##\frac{v_0^2t}{\lambda}##

So in answer to (a), the ##x## and ##y## coordinates of the velocity vector are

$$(v_0, \frac{v_0^2t}{\lambda})$$

Unfortunately, I'm at a loss as to how to tackle (b). I started by differentiating velocity with respect to time, which yields ##\frac{v_0^2}{\lambda}##, but don't know how to proceed from here.