A person throws an object with mass m nearly vertically with an initial momentum p=(px, py, pz). With respect to the cartesian coordinate system where the person is looking in the direction y, with x directed to their right. Let ∝ be the elevation angle of the initial momentum (with respect to the x-y plane) and let θ be the angle of the initial momentum with respect to the y-z plane. Write parametric equations for the trajectory of the center of mass of the object.

How high would the object need to be thrown if three objects are to be juggled at 120 beats per minute (each object is thrown in turn one at a time and one per beat) with a horizontal displacement of approximately 0.30 m? use g = 9.81.