# Free Fall

Helena Dedic

## Understanding Free Fall Motion

• A particle is in a free fall if the gravitational force is the only force acting on it. Note that:

a. the acceleration is equal to g pointing vertically down;
b. we will use ${\displaystyle g=10m/s^{2}}$;
c. we will always choose the positive axis pointing upward and therefore the y-component of the acceleration is always ${\displaystyle a_{y}=-10m/s^{2}}$;
d. the velocity is falling at a rate of 10 m/s every second: e.g., knowing that the velocity is 50 m/s at some time t we can say that 2 s later it will 30 m/s, 5 s later it will be 0 and 8 s later it will - 20 m/s, etc.;
e. a particle is in a free fall (regardless of whether the direction of motion is upward or downward) only if it has no contact with other particles.

Consider an example of a "ball" tossed up: the ball is initially held at rest by the hand; then the hand flips upward and the ball gain upward velocity and at some point fly up in the air, rise to the maximum height, fall down and get caught by the hand coming to rest. Study the diagram and the v - t graph of this event.

• The equations of kinematics for objects in free fall become:

${\displaystyle v_{y}(t)=v_{y0}+(-10)t}$

${\displaystyle \Delta y(t)=v_{y0}(t)+{\frac {1}{2}}(-10)t^{2}}$

${\displaystyle v_{y}^{2}(t)=v_{y0}^{2}+2(-10)\Delta y(t)}$


• Problem solving strategy is similar to the one we used for motion with constant acceleration. Use the following tips when thinking about problems:

o the downward displacement is negative;
o initial velocity is not zero unless an object is dropped (released);
o final velocity is not zero unless we inquire about maximum height;
o final velocity is negative if an object is moving downward.

• The velocity is a linear function and therefore the change of velocity is proportional to time interval e.g., doubling the time interval makes the change of velocity double.

• The displacements is a quadratic function of time. It has a linear term ${\displaystyle v_{0}}$t and a quadratic term ½a${\displaystyle t^{2}}$. It means that the displacement is not proportional to time:

o Displacement during two equal intervals of time are not equal.
o When displacements are equal then the time intervals are not equal.