Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

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Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

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Sensors Sensings

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Faith, Love, Charity

Photosynthesis

Weather

Systems

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Tools

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Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Maximum Height Of A Projectile

The parametrc equatons of the motion of a projectile are as follows:

x = 20t ------(1)

y = -16t^{2} + 30t -------(2)

(a) What is the maximum height of the projectile?

(b) What is the initial velocity of the projectile?

(c) What is the velocity of the projectile when it hits the ground?

(d) What is the range of the projectile?

**The string**:

(a) S_{7}P_{4}A_{42} (Motion - Parabolic).

(b) and (c) S_{7}P_{5}A_{51} (Physical Change - Velocity)

(d) S_{7}P_{4}A_{41} (Linear Motion)
**The math**:

P_{j} Problem of Interest (PPI) is of type *motion*. Problems of distance traveled are *motion problems*.

Vertical velocity of projectile, v = 30 - 32t ---------(3) (derivative of eqn(2))

The projectile attains its maximum height when its vertical velocity, v = 0.

v = 0, when t = 30/32 sec (from eqn(3))

substitute t = 30/32 in eqn (2) to get maximum height of projectile

So, maximum height = 30(30/32) - 16(30/32)^{2} = 14.1 ft

(b) Pj Problem Of Interest (PPI) is of type *change*. Speed, velocity, acceleration and t (duration) problems are *change problems*.

Initial velocity of projectile = 30 ft/sec

(c) Projectile hits the ground when y = 0.

When y = 0, t = 15/8 (from eqn (2)).

Subtituting t = 15/8 in equation (3), we have:

Velociy of projectile when it hits the ground = 30 - 32(15/8) = 30 - 60 = -30 ft/sec.

(d) Pj Problem Of Interest (PPI) is of type *motion*. Distances due to motion are *motion problems*.

The range of a projectile is the horizontal distance from the origin of the projectile to the point when the projectile hits the ground.

So, substituting t = 15/8 in equation (1), we have:

20t =20(15/8) = 75/2 = 37.5

So, range of projectile is 37.5 ft.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings