Formula Sheet

2d Kinematics

Range Formula:

R = (v₀² * sin(2θ)) / g

Airtime for a Projectile (when launched from ground and landing on level ground):

t = 2v0/g

Time for projectile thrown horizontally (or dropped) off a building to reach the ground

t = √(2h/g)

Distance traveled by dropped object:

h = gt²/2

Time of max height of a projectile launched from ground:

t = v0sinθ/g

Total time of flight of a projectile launched from ground:

t = 2v0sinθ/g (time up = time down, so twice as long as the time to reach max height)

Maximum height of a projectile launched from ground:

h = (v0sinθ)² /2g (rearrangement of vf² = (v0sinθ)² - 2gh)

Complementary Angle Formulas w/ same initial launch speed (from papa fon)

  • t1/t2 = tan (theta) (theta being the angle of trajectory 1 with respect to the horizontal)

  • H1/H2 = tan² (theta)

  • t1 * t2 = 2R/g

Dynamics

Terminal Velocity

UCM

F = Gm1m2/r²

First Escape velocity 7.8 km/s

Second Escape velocity is 11 km/s

Third Escape velocity (escape from solar) 16.7 km/s

Escape Velocity Formula

Synchronous orbit:

A synchronous orbit is an orbit in which an orbiting body (usually a satellite) has a period equal to the average rotational period of the body being orbited (usually a planet), and in the same direction of rotation as that body.

Kepler’s First Law

  • All planets orbiting around the sun orbit elliptically

Keplers Second Law

  • The period for a planet

Orbital Velocity

v = √(GM/r)