A program to compare jumping height from two person's lengths.

The calculation uses many simplistic assumptions.

Gravitational energy (E_z) equals mass (m) * gravitational constant (g) * height (h).

E_z = m * g * h

Mass is proportianal to a persons length (l) to the third power.

Energy one's muscles can produce is proportional to a persons length (l) to the second power.

This makes the equation

(c₁ * l²) = (c₂ * l³) * g * h

c₃ = c₂ * g

h = (c₁ * l²) / (c₃ * l³)

c₄ = c₁ / c₃

h = c₄ * l^-1

Relative higher jumping height of the second person equals

Rel_h = (h₂ - h₁) / h₁

h₁ = c₄ * l₁^-1

h₂ = c₄ * l₂^-1

Rel_h = (( c₄ * l₂^-1 ) - ( c₄ * l₁^-1 )) / ( c₄ * l₁^-1 ) = ( l₂^-1 - l₁^-1 ) / l₁^-1

The code in the Texas TI-84 might look like this:


: ClrHome

: Disp "Please enter two lengths."

: Prompt A

: Prompt B

: 100 + ( (100 * (B-1 - A-1)) / A-1 ) -> C

: Disp "B will jump"

: Disp C

: Disp "Percent higher,"

: Disp "compared to A."

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(Texas TI-84 Plus) HigherJump