Initial Velocity Vector and Diagram from Parametric Equation

Oran2009

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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:
[FONT=MathJax_Math-italic]x[FONT=MathJax_Main]([FONT=MathJax_Math-italic]t[FONT=MathJax_Main])[FONT=MathJax_Main]=[FONT=MathJax_Main]0.627273[FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]0.211364[/FONT][FONT=MathJax_Main])[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]
[FONT=MathJax_Math-italic]y[FONT=MathJax_Main]([FONT=MathJax_Math-italic]t[FONT=MathJax_Main])[FONT=MathJax_Main]=[FONT=MathJax_Main]−[FONT=MathJax_Main]0.658275[/FONT][FONT=MathJax_Math-italic]t[FONT=MathJax_Main]2[/FONT][/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]1.96578[/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]0.014545[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]​
I have found that the initial velocity vector is:
[FONT=MathJax_Math-italic]v[FONT=MathJax_Main]2[FONT=MathJax_Main]=[FONT=MathJax_Main]0.627273[FONT=MathJax_Main]2[FONT=MathJax_Main]+[FONT=MathJax_Main]1.96578[FONT=MathJax_Main]2[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]
[FONT=MathJax_Math-italic]v[FONT=MathJax_Main]=[FONT=MathJax_Main]2.06343461853[/FONT][/FONT][/FONT]
[FONT=MathJax_Math-italic]v[FONT=MathJax_Main]([FONT=MathJax_Math-italic]t[FONT=MathJax_Main])[FONT=MathJax_Main]=[FONT=MathJax_Main]([FONT=MathJax_Main]0.627273[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Main]1.96578[/FONT][FONT=MathJax_Main])[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]​
Firstly, is this correct?

Secondly, we are required to make a diagram showing the initial velocity vector and the components. How am I to do this accurately on the graph (in Desmos)?
 
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:
[FONT=MathJax_Math-italic]x[FONT=MathJax_Main]([FONT=MathJax_Math-italic]t[FONT=MathJax_Main])[FONT=MathJax_Main]=[FONT=MathJax_Main]0.627273[FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]0.211364[/FONT][FONT=MathJax_Main])[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]
[FONT=MathJax_Math-italic]y[FONT=MathJax_Main]([FONT=MathJax_Math-italic]t[FONT=MathJax_Main])[FONT=MathJax_Main]=[FONT=MathJax_Main]−[FONT=MathJax_Main]0.658275[/FONT][FONT=MathJax_Math-italic]t[FONT=MathJax_Main]2[/FONT][/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]1.96578[/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]0.014545[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]​
I have found that the initial velocity vector is:
[FONT=MathJax_Math-italic]v[FONT=MathJax_Main]2[FONT=MathJax_Main]=[FONT=MathJax_Main]0.627273[FONT=MathJax_Main]2[FONT=MathJax_Main]+[FONT=MathJax_Main]1.96578[FONT=MathJax_Main]2[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]
[FONT=MathJax_Math-italic]v[FONT=MathJax_Main]=[FONT=MathJax_Main]2.06343461853[/FONT][/FONT][/FONT]
[FONT=MathJax_Math-italic]v[FONT=MathJax_Main]([FONT=MathJax_Math-italic]t[FONT=MathJax_Main])[FONT=MathJax_Main]=[FONT=MathJax_Main]([FONT=MathJax_Main]0.627273[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Main]1.96578[/FONT][FONT=MathJax_Main])[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]​
Firstly, is this correct?

Secondly, we are required to make a diagram showing the initial velocity vector and the components. How am I to do this accurately on the graph (in Desmos)?
[FONT=MathJax_Math-italic]v[FONT=MathJax_Main]2[/FONT][/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]0.627273[FONT=MathJax_Main]2[/FONT][/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]1.96578[FONT=MathJax_Main]2 ................ What is v2?[/FONT][/FONT]​
 
The parametric equations are x(t)=0.627273t+(−0.211364) and y(t)=−0.658275t^2+1.96578t+0.014545.

Then x'(t)= 0.627273 and y'= -1.31655t+ 1.96578.
Assuming that "t" is "time" (you didn't actually say it was but otherwise this problem is impossible) then that is the velocity vector.

The "initial velocity" vector, at t= 0 is <0.627272, 1.97579>. You have written that as "v2= 0.627272+ 1.97579". I don't know what you mean by "v2" but that is not a vector at all.

Are you required to use desmos? Since desmos does not have a facility for drawing line segments, it would be much easier just to do it "by hand".
 
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