Two Particles P₁ and P₂ Are Moving in the Plane $x ^ { 2 } + y ^ { 2 } = 1$

question 7

Essay

Two particles p₁ and p₂ are moving in the plane, with p₁ moving vertically upward from initial point (0,0)and p₂ moving around the unit circle $x ^ { 2 } + y ^ { 2 } = 1$ with initial point (0, 1)in the counter-clockwise direction.
(a)Choose parameterizations for p₁ and p₂ so that the two particles collide at the point of intersection of their paths.
(b)If the sum of the speeds of these two particles is greater than 3 at the time of collision, then the two particles combine to become one.Will this happen with your chosen parameterization?

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Definitions:

Nominal Variables

Factors that denote classifications without any inherent hierarchy or sequence.

Dummy Variables

Binary variables created to represent categorical data in order to use such variables in regression analysis.

Nominal Variable

A type of categorical variable for which there is no inherent order or ranking among the categories.

Indicator Variables

Variables used in regression analysis that take on the value of 0 or 1 to indicate the absence or presence of a categorical effect that may be expected to shift the outcome.