Question

I must calculate the tangential acceleration and the normal acceleration of a two-dimensional trajectory at a given time: a = a(tan) + a(norm) =d(v)/dt *e(tan) + v * d(e(tan))/dt. I just don't know how to take the derivatives in this case.

Answer 1

Do you know the position function \( \vec x(t) \)?

Answer 2

The position vector is (v(o) cos(beta(0)), v(0) sin(beta(0)) – gt). As a numerical result I have a(norm(t1)) = g cos(beta(1)) and a(tan(t1)) = g sin(beta(t1)). I don’t know how he got these results.

Answer 3

To clarify, you're saying that
\[ \vec x(t) = v_0 \cos(\beta_0)\hat x + \left(v_0 \sin(\beta_0) - gt\right) \hat y \]
is that correct?

Answer 4

Or do you mean
\[ \vec x(t) = v_0 \cos(\beta t) \hat x + \left( v_0 \sin(\beta t) - gt\right) \hat y \]
?

Answer 5

see the attached diagram for a hint