PASCO ME-6825A MINI LAUNCHER - Manual (Page 35)

012-05479B Mini Launcher
33
®
Experiment 8 (Demo): Do 30
⋅⋅⋅⋅⋅ and 60⋅⋅⋅⋅⋅ Give the Same Range?
EQUIPMENT NEEDED
-Mini Launcher and steel ball
Purpose
The purpose of this demonstration is to show that the range of a ball launched at 30° is the same as
one launched at 60° if the ball is shot on a level surface.
Theory
The range is the horizontal distance, x, between the muzzle of the Launcher and the place where
the ball hits, given by x = (v
0
cos
θ)t where v
0
is the initial speed of the ball as it leaves the muzzle,
θ
is the angle of inclination above horizontal, and t is the time of flight.
If the ball hits on a place that is at the same level 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 the reach the peak of its trajectory:
where g is the acceleration due to gravity.
Substituting for t into the equation for x gives
and using a trigonometry identity gives
The ranges for the angles 30° and 60° are the same since sin(60°) = sin(120°).
Setup
➀
Clamp the Mini Launcher near one end of a sturdy table with the Launcher aimed so the ball will
land on the table. See Figure 8.1.
➁
Adjust the angle of the Mini Launcher to 30 degrees.
➂
Put the steel ball into the Mini Launcher and cock it to the medium or long range position.
Procedure
➀
Shoot the ball at 30 degrees to find
where the ball lands.
➁
Change the angle of the Launcher to 60
degrees and shoot the ball again. Call
attention to the fact that the ball again
lands in the same place. Thus the
ranges are the same.
➂
Change the angle to 45 degrees and
shoot the ball again to show that the
ball now lands further away.
➃
Ask the question: What other pairs of angles will have a common range? This demonstration can
be done for any two angles which add up to 90 degrees: 20 and 70, or 35 and 55, etc.
Figure 8.1: Setup to shoot on level surface
t = 2t
peak
= 2
v
0
sin
θ
g
x =
2v
0
2 sin
θ cosθ
g
x=
v
0
2 sin2
θ
g