Show that for t > 0, the Cartesian equation of the path of P is given by 4x2 + (y+1)2 = 4z.

Here's the solution to the problems you sent:

Question 1:
The position vector of a particle P of mass 2kg at time $t$ is given by $\mathbf{r} = [(t \cos t) \mathbf{i} + (2t \sin t - 1) \mathbf{j} + t \mathbf{k}] \, \text{m}$.

i) Show that for $t > 0$, the Cartesian equation of the path of P is given by $4x^2 + (y+1)^2 = 4z$.

Step 1: Identify the components of the position vector.
From the given position vector $\mathbf{r} =