Free Fall

near the Earth’s surface, an object dropped from a moderate height falls

vertically with a constant acceleration

• due to gravity, g = 9..80 m/s² (little g)

• g is valued only if we neglect air resistance

  • air has an effect on the motion of the falling object

constant acceleration in the vertical direction

still a one-dimensional vector

• y is the distance of the fall and is positive in the upward direction, and thus an object falling has a vector g = -g y-hat

  • acceleration a = -g = -9.80 m/s²

motion with constant acceleration in the vertical direction occurs by

replacing a with -g in the equations vt = v0 + at and xt = x0 + v0t + ½ at² (equations for constant acceleration, since g is constant)

• vt = v0 - gt (velocity with acceleration being -g = -9.80 m/s² in free fall)

• yt = y0 + v0t - ½ gt² (position with acceleration being -g = -9.80 m/s² in free fall in the vertical direction)

• these are equations for the fall of an object in the absence of air resistance

vt = v0 - gt

velocity becomes more downward (-y) as time goes by, and acceleration of -g is constant

yt = y0 + v0t - ½ gt²

displacement in the vertical direction depends on the initial velocity and time, since acceleration of -g is constant

for the time of descent, when two objects with similar shapes but different mass are abandoned simultaneously from the same height,

both objects will reach the ground at the same time

• proposed by Galileo Galilei

• acceleration for free fall is constant and does not depend on mass

using kinematics, we can derive the expression for the

time taken by a dropped object to reach the ground

• yt = y0 + v0t - ½ gt²

• if y0 = h and yt = 0, then 0 = h + v0t - ½ gt²

  • if v0 = 0, then 0 = h - ½ gt², and thus h = ½ gt²

    • t² = 2h/g, and thus t = √2h/g

• valid only in the absence of air resistance, and the time for free fall is independent of the mass of the object