nerdamer.physics_example.js

/*
https://sciencenotes.org/projectile-motion-example-problem-physics-homework-help/
A cannon is fired with muzzle velocity of 150 m/s at an angle of elevation = 45°. Gravity = 9.8 m/s2.
a) What is the maximum height the projectile reaches?
b) What is the total time aloft?
c) How far away did the projectile land? (Range)
d) Where is the projectile at 10 seconds after firing?
*/
var knowns = {
    v0: 150, // m/s
    theta: 45, // deg
    g: 9.8 // m/s^2
};

//assuming degrees
var eqs = {
    vx: 'v0*cos(radians(theta))',
    vy: 'v0*sin(radians(theta))-g*t',
    x: 'v0*t*cos(radians(theta))',
    range: 'v0*t_total*cos(radians(theta))',
    y: 'v0*t*sin(radians(theta))-0.5*g*t^2'
};

//at the top velocity is zero so we can add that to the knowns
var t = nerdamer(eqs.vy, knowns).solveFor('t')[0];
console.log(`time: ${t.text()} seconds`);
knowns.t = t;

// a)
var max_height = nerdamer(eqs.y, knowns).evaluate().text();
console.log(`max height: ${max_height} meters`);

// b)
var time_aloft = nerdamer(knowns.t).multiply(2).evaluate().text();
console.log(`time aloft: ${time_aloft} seconds`);

//make a note of total time in the air
knowns.t_total = time_aloft;

// c)
var Range = nerdamer(eqs.range, knowns).evaluate().text();
console.log(`Range: ${Range} meters`);

// d)
knowns.t = 10;
var x10 = nerdamer(eqs.x, knowns).evaluate().text();
var y10 = nerdamer(eqs.y, knowns).evaluate().text();
console.log(`At 10 seconds: x is ${x10} meters and y is ${y10} meters`);