Problem 2. (6 points) A particle is moving along the surface of a paraboloid z = 1:2 + 332. The motion is such that the particle completes a full revolution around the zaxis in 1 seconds with some uniform angular velocity around zaxis. Moreover, with each such full revolution completed, the particle unifonnly move along +z axis by 1 unit. Find the parametric equation E of the trajectory in terms of the time parameter given that m = (D, 0, } and find II :5 II = (1,0,0) _, p r 1. Let the constant uniform angular velocity be to. This means that do? : was where it denotes change. Similarly, uniform motion along +z axis with respect to particle's revolution is the same as saying that $2. = cos. Find the constants c and w from the information provided. 2. We can now express both 19 and 2. as a function of time using the constants found above assuming some initial Hg and 0 at in = 0. Write down those expressions. Recall that equation of a paraboloid in cylindrical coordinates is given by r : 1/3. Find 1" as a function of time. 3. Use the given initial condition to find Zn and {in and give the final parametric equation of the curve with parameter r as time starting from t = D with location [I], l], U}