The Horizontal and Vertical Velocity Components calculator computes the vertical and horizontal components of a velocity vector defined by a magnitude (initial velocity) and direction (launch angle).

INSTRUCTIONS: Choose units and enter the following:

• (V) Velocity Magnitude
• (θ) Launch Angle

Horizontal and Vertical Velocity Components (V_x , V_y): The calculator returns the components in meters per second.  However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The vertical and horizontal velocity components equation calculates the horizontal (x) and vertical (y) components of initial velocity given the initial velocity vector magnitude and the launch angle.

V_x = V₀*cos(θ)

V_y = V₀*sin(θ)

Inputs:

• V₀ - initial velocity magnitude
• θ - launch angle above the local horizontal
• V_X = Horizontal Component
• V_Y = Vertical Component

Vector Calculator

3D vector arithmetic functions including Cartesian, Spherical and Cylindrical coordinate transforms.

• k V - scalar multiplication
• V / |V| - Computes the Unit Vector
• |V| - Computes the magnitude of a vector
• U + V - Vector addition
• U - V - Vector subtraction
• |U - V| - Distance between vector endpoints.
• |U + V| - Magnitude of vector sum.
• V • U - Computes the dot product of two vectors
• V x U - Computes the cross product of two vectors
• V x U • W - Computes the mixed product of three vectors
• Vector Angle - Computes the angle between two vectors
• Vector Area - Computes the area between two vectors
• Vector Projection - Compute the vector projection of V onto U.
• Vector Rotation - Compute the result vector after rotating around an axis.
• Normal to 3 Points - Vector Normal to a Plane Defined by Three Points
• (ρ, θ, φ) to (x,y,z) - Spherical to Cartesian coordinates
• (x,y,z) to (ρ, θ, φ) - Cartesian to Spherical coordinates
• (r, θ, z) to (x,y,z) - Cylindrical to Cartesian coordinates
• (x,y,z) to (r, θ, z) - Cartesian to Cylindrical coordinates
• Vector Components - Magnitude, Unit Vector and angle between vector and three coordinate axes

Statistics Calculator

• Observational Stats:  This function accepts a table of numbers separated by commas and calculates observational statistics for any of the columns.  This includes count, min, max, sum, sum of squares (Σx²), square of the sum (Σx)², mean, median, mode, range, mid point, rand, sort up, sort down, rand, population variance, population standard deviation, the sample/experimental variance, sample/experimental standard deviation.
• Frequency Distribution:  This function lets you enter a string of numbers separated by commas, a low and high range and a number of bins.  It then computes how many of the observations are in each of the bins between the high and low values designated. 
• Random Sample (k):  This generate a random sample of k items within a set.
• Percentile:  This computes the relative percentile of an observation verses a set.
• P(A) = F / T: This computes the probability of a favorable event in a total number of outcomes.
• P(n,S) - Binomial Probability:  Probability of S successes in n trials of a binomial distribution.
• Binomial Coefficient: from Pascal's Triangle. 
• zSCORE (y in X):  This computes the z SCORE of an observation in a set (X).
• zSCORE (y,μ,σ):  This computes the z SCORE of an observation based on the mean and standard deviation.
• z from P(y):  This computes the z SCORE based on a probability or percentile in a Normal Distribution table.
• P(y) left of z: This computes the percentile, probability or area under the curve of a Normal Distribution left of the z SCORE.
• P(y) right of z: This computes the percentile, probability or area under the curve of a Normal Distribution right of the z SCORE.
• Probability between z SCORES:  This computes the area under the Normal Distribution curve between z SCOREs.
• Raw Score (P,μ,σ): This computes the raw score associated with a percentile in a Normal Distribution (μ,σ).
• Paired Sample t-test:  This computes the various parameters associated with the Paired Sample t-test.
• y = a + bx:  This is linear equation used with Linear Regression to predict values of Y.
• ANOVA (one way): The is one way analysis of variance
• (χ²) Chi-Square Test: This computes the Chi-Square value for an nxm array of data and provides the degrees of freedom.
• Linear Regression:  This computes the regression line (least-squares) through a set of X and Y observations.  It also computes the regression coefficient (r).

Quaternion Calculator

• Quaternion Addition
• Quaternion Subtraction
• Quaternion Multiplication
• Quaternion Magnitude
• Quaternion Versor
• Quaternion Conjugate
• Quaternion Inverse
• Quaternion of Rotation
• Vector Rotation

3x3 Matrix Characteristics: computes the determinant, trace, inverse and characteristic polynomial of a 3x3 matrix, Cramer’s Rule