University Of Arizona

PHYS 181 Range versus Height Lab Report
Course: PHYS 181-001-14
Abstract
In this experiment, we measured the range (the horizontal distance) that an object
traveled when dropped from a height of 20 cm before coming in contact with a bounce plate at
an angle of 45°. After 18 trials, our results showed that the ball had an average range of 28.48 cm
when dropped from 20 cm, with a standard deviation of 1.2 cm. At first, we used the method of
just dropping the ball through the hole of the platform by hand, but we found our second method
was more reliable (placing a ruler under the hole of the drop plate and quickly pulling it out from
under, allowing the ball to fall). With this new method, our standard deviation at 20 cm was 0.72
cm. We then measured the range when the ball was dropped from different heights (5 cm, 10 cm,
15 cm, 20 cm, 25 cm, and 30 cm) using this new method, and we plotted the average range
versus height in √cm . We got a slope of 6.68.
Introduction
In this lab, we measured the range of a ball bearing after dropping it onto a bounce plate
from different heights for 18 trials at each height. In part one of the lab, the ball was dropped 20
cm above the bounce plate for 18 trials. After 18 trials, the three extreme upper and lower
deviations were removed, and with these remaining 12 data points, we found the standard
deviation. In part two, we used a different method measuring at the same height (20 cm) in order
to determine which method is more precise. After repeating the same steps in part one, we found
a standard deviation using this method and compared it with the standard deviation from part
one. In part three, we used the more precise method to make measurements when dropping the
ball from different heights in order to graph the relationship between distances traveled versus
height √cm at which the ball was dropped. We will use the equations (vf2 = vo2 + 2ayy), (y =
Vot – 1/2gt2), (x = xo + voxt) and (vx = vox) to determine the relationship between range and height.
Theory
After collecting measurements of the distance the ball traveled versus its height in
√cm , we were able to graphically see a linear relationship between range versus height. In
order to demonstrate this relationship mathematically, we begin with an equation relating to the
vertical component of the ball’s motion:
vf2 = vo2 + 2ayy
Knowing that (y = y - yo), after re-arranging the equation to solve for vf, the equation looks like
this:
vyf = √Vyo+2ay ( y- yo )
The acceleration in the y-component is equal to gravity (g), which is -9.8 m/s2. The ball is
dropping from rest, so its vyo is equal to 0 m/s. Also, we can replace y - yo with “h” since that is
the height between the drop plate and the bounce plate:
Equation 1: vyf = √2gh