Name ______Period _____

Lab: Determining the Range of a Horizontal Projectile

Purpose: To find out if the motion equations really work for determining projectile range.

Procedure: We will be comparing the actual range that we measure for a ball that is launched off a ramp

horizontally to the range that we calculate for that ball using motion equations.

To perform the experiment:

·  Clamp the launch ramp to the very edge of the table.

·  Measure and record the distance “D” from the overhang edge of the ramp to the floor

·  Tape your data sheet of paper (approximately 50 cm x 100 cm) with the carbon paper placed face down over it to the floor with approximately 10 cm of paper under the table, and the rest extending out from the table edge along the flight path as shown.

·  Use a plumb line (paper clip tied to thread) held at the end of the ramp to mark the paper directly beneath the launch point at the end of the ramp with a dot. This is your starting point for the actual range distance. Label the dot with “Start”

·  Start the ball at the top of the ramp and measure the vertical distance from the ramp top to the table top. Record this distance in the “H” column of your data table.

·  Measure the length “L” along the table from beneath the release point on the ramp to the launch point.

·  Calculate and record the angle q of the ramp using tangent of q = H/L

·  Release the ball from the very top of the ramp, and after it hits the floor, lift up the carbon paper and write “trial #1” next to the carbon dot mark on the paper.

·  Cross out any marks left by ball bounces.

·  Measure and record the range of the ball on your data sheet and in your data table

·  Repeat the last six steps four more times, starting the ball at a different place on the ramp above the table each time. Record each new ramp height above the table and label each new paper mark with its trial number immediately after the ball hits.

·  Calculate the launch velocity vox of the ball coming off the ramp for each trial using the motion equation: vf2 = 2g(sin q)H. ( vf in this equation will actually be the starting velocity vox for the projectile part of the motion.)

·  Calculate the time t for the projectile motion using D = ½ at2 . D is the distance from the table top to the floor.

·  Calculate the range dx for each trial using the motion equation dx = vot

·  Compare your calculated values for dx to the ones you actually measured using a percent difference calculation with the measured range as the actual value.

Data Table: Distance from table top to floor: D (cm) ______D (m)______

Trial / H (m)
Ramp top to table top / L(m)
Along table
Top beneath
ramp / dx (m)
measured
range / q
Tan-1
(H/L) / g(sin q) / vox (m/s)
(vf for ramp is vox for launch) / t (s)
for fall
to ground / dx (m)
calculated
range / % Difference
of ranges

Sample Calculations:

Quantity calculated / Formula Used / Substitution using your data / Answer with Units
cm to meters / cm/100 = m
q for ramp / tan-1 (H/L)
a for ramp / a=g sin q
Launch vox (m/s)
(vf coming off table) / vf2 = 2aH
t (s)
(for fall to ground) / D = ½ gt2
dx (m)
(calculated range) / dx = voxt
(vf ramp = vox launch)
% Difference
of ranges / % Diff = ( meas. dx – calc. dx) (100)
( meas. dx)

Questions:

1.  Overall, how did your actual ranges (measured dx values) compare to your calculated ranges? (smaller, larger, not anything like, the same)

2. What are three different factors that might have caused the differences between your measure range

value and your calculated range value?

a.

b.

c.

3. Explain specifically (according to your average results using a demonstration calculation and diagrams

if necessary) how each factor you mentioned above in answer to question #2 would have affected your

percent difference. For example, if you mis-measured a value, estimate by how much you would have

mis-measured it and show how your calculation of the quantity and the resulting percent difference

based on that measurement would be affected.

Factor a:

Factor b:

Factor c:

4. Do you believe that the motion equations work for giving realistic values for projectile ranges?

Justify your answer.