Provide an Appropriate Response By Solving the Following Initial Value Problem for a Vector

question 54

Essay

Provide an appropriate response.
-Derive the equations
$\begin{array} { l } x = x _ { 0 } + \left( v _ { 0 } \cos \alpha \right) t \\y = y _ { 0 } + \left( v _ { 0 } \sin \alpha \right) t - \frac { 1 } { 2 } g ^ { 2 }\end{array}$
by solving the following initial value problem for a vector $\mathbf { r }$ in the plane.
Differential equation $\frac { \mathrm { d } ^ { 2 } \mathbf { r } } { \mathrm { dt } ^ { 2 } } = - \mathrm { gj }$ Initial conditions:
$$\begin{array} { l } \mathbf { r } ( 0 ) = \mathrm { x } _ { 0 } \mathbf { i } + \mathrm { y } _ { 0 } \mathbf { j } \\\left. \frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } ( 0 ) = \mathrm { v } _ { 0 } \cos \alpha \right) \mathbf { i } + \left( \mathrm { v } _ { 0 } \sin \alpha \right) \mathbf { j }\end{array}$$

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Definitions:

Ethology

The scientific study of animal behavior, often with a focus on behavior under natural conditions, and viewing behavior as an evolutionarily adaptive trait.

Frustration-Aggression Hypothesis

Originally the idea that aggression is always preceded by frustration and that frustration inevitably leads to aggression. Revised to suggest that frustration produces an emotional readiness to aggress.

Emotional Readiness

An individual's preparedness to experience, manage, and appropriately express emotions in a given situation or in response to specific challenges.

Frustration

A feeling of disappointment and dissatisfaction arising from the hindrance of achieving a goal.