# (Texas TI-84 Plus) HigherJump

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

The calculation uses many simplistic assumptions.

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

Ez = 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

Relh = (h2 - h1) / h1

h1 = c4 * l1-1

h2 = c4 * l2-1

Relh = (( 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." ``` This page has been created by the tool CodeToHtml