I have the following:
- 2d vector for velocity
- 2d start coordinate
- gravity acceleration
I need to know the coordinate of a projectile at a given distance along the trajectory.
For example:
- Velocity = (5m/s,3m/s)
- start coordinate = (10m,10m)
- gravity = 10m/s/s
- distance along trajectory from start = 1m
I'm doing this for a simulation where I need to draw a dotted line along a trajectory of a projectile.
Taking $y$ as the vertical, measured up, and $x$ as horizontal, we have $x(t)=x_0+v_x(0)t, y(t)=y_0+v_y(0)t-\frac{g}{2}t^2$
Added: the arclength element is $ds=\sqrt{dx^2+dy^2}$ so $\frac{ds}{dt}=\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}=\sqrt{v_x^2+(v_y(0)-gt)^2}$ It may be easier to integrate the differential equation, particularly if something may perturb the trajectory along the path.