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`V_x = V * cos( theta )`
Enter a value for all fields
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 (Vx , Vy): 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.
Vx = V0*cos(θ)
Vy = V0*sin(θ)
Inputs:
- V0 - initial velocity magnitude
- θ - launch angle above the local horizontal
- VX = Horizontal Component
- VY = 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