Physical Science Lab #3
Projectile Motion
Theory
For an object falling with no horizontal motion in earth's gravity in such a away that we can
ignore air resistance, its motion up and down is described by y = voyt
+ 1/2 gt2, where y is the position relative to the starting position,
vo is the starting velocity, t is the time and g is the acceleration due to
gravity (g = 9.8 m/s2). Down is considered the positive direction for this equation. This equation is also valid for describing the up and down (vertical) motion of an object traveling in a parabolic arc. The back and forth (horizontal) motion is much simpler because there is no accleration horizontally, so the velocity (vox) is constant and x = voxt describes the horzontal position, x.
From trigonometry we can figure out how tall something is if we know how far we are from the
base
of the object and we measure the angle from the base to the top of the object. From
trig we get:
height = distance to base x tan(angle)
Procedure
We will use the funnelator (a giant slingshot) to shoot a rubber ball upward. We will use trigonometry to figure out the height of the ball at maximum and then time the duration of the fall until it hits the ground. We will do a number of launches
- Choose a launching station and then shoot the ball upward to find the approximate height it goes. Measure off about that distance to the viewing station.
- When the ball is launched one partner should sight along a meter stick and hold the stick in place where the maximum height occurs. At this point the timer should start the stop watch and stop it when the ball hits ground. Then measure the angle the meter stick makes with the ground. Your data table will have: distance to base, angle and time.
- We will do some angled launches to get a view of a parabolic trajectory.
Calculations
At the peak of the ball's path it has zero velocity so our equation simplifies as in the last lab. The distacne it travels down in the time measured is given by the trig equation in the theory section. Calculate the theroetical height from the time using the first equation abd compare it the result measured via trigonometry (this is actually an experimental result though we do rely on the theories of trig to get it.) Discuss the results.