PASCO ME-6831 Ballistic Pendulum_Projectile Launcher - Manual (Page 47)

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M o d e l N o . M E - 6 8 3 0 E x p . 1 0 ( D e m o ) : D o 3 0 ° a n d 6 0 ° G i v e t h e S a m e R a n g e ?
0 1 2 - 0 5 3 7 5 C 43
Exp. 10 (Demo): Do 30° and 60° Give the Same Range?
Equipment Needed
Purpose
The purpose of this demonstration is to confirm that the range of a ball launched at 30° is the same as one launched
at 60° if the ball lands at the same height from which it was launched.
Theory
The range is the horizontal distance, x, between the muzzle of the Launcher and the place where the projectile
lands, given by x = (v
0
cos
) t where v
0
is the initial speed of the ball as it leaves the muzzle,
 is the launch angle
above horizontal, and t is the time of flight.
If the ball lands on a target that is at the same height as the level of the muzzle of the launcher, the time of flight of
the ball will be twice the time it takes the ball to reach the peak of its trajectory, when its vertical component of
speed reaches zero.
where g is the acceleration due to gravity. Substituting for t in the equation for x gives:, and t is the time of flight.
and using a trigonometry identity gives:
The ranges for the angles 30° and 60° are the same since sin 60° = sin 120°.
Setup
1. Clamp the Projectile Launcher to a sturdy
table. Mount the Launcher near one end of
the table with the Launcher aimed toward
the middle of the table.
2. Adjust the angle of the Launcher to 30°.
3. Put the steel ball into the Launcher and cock
it to the medium range or long range setting.
• NOTE: In general, this demonstration will
not work as well on the short range setting because the muzzle speed is more variable with the change in
angle.
4. Fire a test shot to see where the ball hits. Place the box in front of that location so that the next ball will hit the
top of the box.
Procedure
1. Shoot the ball at 30° to demonstrate that the ball lands on the box.
Item Item
Projectile Launcher and steel ball Box to make landing area same height as muzzle
t 2t
peak
2v
0

sin
g
-------------------- = =
x
2v
0
2  
cos sin
g
-------------------------------- =
x
v
0
2
2

sin
g
-------------------- =
CAUTION! DO NO T LOO K
DOW N BARREL! CAUTION! DO NO T LOO K
DOW N BARREL! CA UT ION !
DO NO T L OO K
DO WN TH E B AR RE L. LO NG RA NG E
ME DIU M RA NG E
SH OR T RA NG E Position of Ball
Laun ch
SH OR T R AN GE
PROJECTILE LAUNC
HER
ME -68 00
Ye llo w B an d i n W ind ow
Ind ica tes Ra ng e.
90 80 70 60 50 40 30 20 10 0
WE AR SA FE TY
GL AS SE S
WH EN IN US E.
Us e 2 5 m m
ba lls ON L Y!
Figure 10.1: Set up to shoot on level surface.
Box