Gravity is quadratic.
Everything on Earth (buildings, airplanes, us) is struggling against its unrelenting downward pulling force.
Including anything you toss/shoot up.
-16t2 + v0t + h0
height (in feet) of an object (ball, bullet, rock etc)
thrown/fired straight up with initial velocity v0 (in feet per second)
from an initial height h0 (in feet) above the ground
t seconds after launch
(ignores air resistance!)
-16t2 + 10t + 50
initial velocity: 10 ft/s starting height: 50 ft above ground
What is the object's height after t= 1, 2, 3 seconds?
-16t2 + 146t
initial velocity: 146 ft/s (about 100MPH) from ground (h0=0)
What is the object's height after t= 1...10 seconds?
-16t2 + 500
initial velocity: 0 ft/s (v0=0 i.e. dropped) 500 ft above ground
What is the object's height after t= 1...6 seconds?
Height is 0 when the object has landed.
-16t2 + v0t + h0 = 0
Solving this quadratic equation gives the value(s) of t when the object is on the ground.