Projectile Attack Lab
Introduction:
The purpose of this lab is to be able to launch a projectile from a table so that it hits a
target below. The projectile will by launched from a ramp that can be set at varying
angles to control the speed of the projectile – a steel marble. The target can be anywhere
within a range of distances that will not be known until immediately before the launch.
Achieving this objective requires an understanding of projectile motion. A projectile is
any object traveling through the air with no means of propelling itself. It’s path, or
trajectory, is parabolic. A projectile is an example of two-dimensional motion. It’s
motion can be analyzed as the combination of a horizontal motion (x – direction) and a
vertical component (y- direction). These two components of motion are independent of
each other. So it’s motion in the y direction is not affected by it’s motion in the x
direction.
In the y direction, the projectile is falling under the influence of gravity. If it is launched
horizontally, its initial velocity in the y direction is 0 m/s. The equation Δy = ½gt2 relates
falling distance and time. So if the height of the launch is known, the time can be
calculated (since g = 9.8 m/s2). In the x direction, there is no gravity or force affecting
the velocity, so v is constant. The projectile will continue at a constant velocity until it
hits the ground. So the displacement in the x direction can be calculated using the
equation Δx = vt. The two components of motion are related only by the time.
So if the height of the launch is known, the horizontal distance it travels can be controlled
by changing the horizontal velocity.
Hypothesis:
If the height of the ramp is increased, the horizontal velocity of the projectile will
increase – the graph of the relationship between these two will follow a best fit line that
will flatten out as the angle of the ramp approaches 90 degrees.
Procedure:
Materials: metal ramp, 2.5 cm steel marble, photogates master and slave unit, meter
stick.
The ramp was set as shown in the diagram below with one end at an initial height of 5
cm. The master photogate and slave were set 10 cm apart. In each trial, the marble was
released from a set point at the top of the ramp. The photogates measured the time for
the ball to pass between the two gates. The velocity of the ball was therefore v = d/t or,
for each trial v = 10 cm/t measured. Six trials were performed at different heights
between 5 cm and 20 cm. The ramp had to be at least 5 cm from the mater photogate to
eliminate the effect of the ball bouncing as it hit the table,
Procedure:
Apparatus:
Master
photogate
height
slave
10 cm
91 cm
Data:
The distance from the table to floor: 91 cm
The ramp height, times recorded and distance velocity are shown in the table below.
Column 1 is the height of the ramp, column 2 is the time recorded for the ball and column
3 is the velocity calculated as v = 10 cm/t
Table 1
height (cm)
5
10
15
20
25
time (s)
0.14
0.10
0.09
0.08
0.07
velocity
v= 10 cm/t
72.34
95.45
112.26
125.95
137.71
Analysis and Calculations:
Calculate the time for the projectile to fall 91 cm from the table top to the floor:
Δy = ½gt2
0.91m = ½(9.8 m/s2)( t2)
solve for t
t = 0.43 s
Since this is the time that the projectile is also traveling at a constant velocity in the
horizontal direction, the distance for each horizontal velocity can be calculated as:
Δx = vt
where v = velocity from table 1 col. 3 and t = 0.43 s.
There results are shown in table 2 below. Graph 1 shows the relationship between height
(col. 1) and the horizontal distance, Δx predicted.
height (cm)
5
10
15
20
25
time (s)
0.14
0.10
0.09
0.08
0.07
velocity
v= 10 cm/t
72.34
95.45
112.26
125.95
137.71
distance
d = 0.43(v)
31.11
41.04
48.27
54.16
59.21
The graph shows a relationship between the height of the ramp and the distance that the
projectile will travel that is exponential and begins to flatten out as the ramp height
exceeds 25 cm.
When given a target distance, the best fit line shown on the graph will show the proper
ramp height to hit the target.
Our target distance was 39 cm – using the graph, a corresponding height of 8 cm was
found as shown on graph 1. The launch was hit within the target area.
Conclusion:
The hypothesis that there was a predictable relationship between height of the ramp and
the distance the ball would travel based on the analysis of the motion of a projectile
proved to be correct. The analysis successfully predicted the distance traveled be the
projectile within a reasonable error. The main sources of error in this lab were the
precision of the height and distance measurements. Using a meter stick these were
limited to plus or minus about 1 cm. Also, the assumption that horizontal velocity is
constant ignores the affect of friction on the table and air resistance. These would
actually slow the projectile. Friction can be minimized by keeping the distances on the
table as shot as possible. Air resistance is probably very small, This might be reduced
by using a smaller sphere.