- #1
marksyncm
- 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.