Initial Velocity Vector and Parametrics

Question

I have a project where we have to throw an object and find the velocity of it. I have found the parametric equations of the path of the object to be: $$x(t) = 0.627273t + (-0.211364)$$ $$y(t) = -0.658275t^2 + 1.96578t + 0.014545$$

Here is the graph:

Now, we are supposed to find the vector components and then calculate the initial velocity vector, without using physics formulas. How would I approach doing this?

Answer 1

HINT

Recall that the velocity vector is given by

$$v(t)=(\dot x(t),\dot y(t))$$

with

• $\dot x(t)=\frac{dx}{dt}\approx \frac{\Delta x}{\Delta t}$
• $\dot y(t)=\frac{dy}{dt}\approx \frac{\Delta y}{\Delta t}$