Pasco Scientific ME-6825, Инструкция по эксплуатации и руководство по экспериментам

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012-05479A Mini Launcher
15
Experiment 3: Projectile Range Versus Angle
θ
x
v
0
Figure 3.1: Shooting on a level surface
θ
x
v
0
y
0
Figure 3.2: Shooting off the table
EQUIPMENT NEEDED
– Mini Launcher and steel ball – Plumb bob
– Measuring tape or meter stick – Carbon paper
– Graph paper – White paper
Purpose
The purpose of this experiment is to find how the range of the ball depends on the angle at
which it is launched. The angle that gives the greatest range is determined for two cases:
launching on level ground and launching off a table.
Theory
The range is the horizontal distance, x, between the muzzle of the Launcher and the place
where the ball lands. The range is 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. See figure 3.1.
For the case in which the ball lands at the same elevation from which it was launched, the time
of flight of the ball will be twice the time it takes the ball the reach the peak of its trajectory. At
the peak, the vertical velocity is zero so
v
y
= 0 = v
0
sin θ – gt
peak
Therefore, solving for the time gives the total time of flight as t = 2 t
peak
= 2
v
0
sin
θ
g
.
For the case in which the ball is
launched at an angle from a table
onto the floor, (See Figure 3.2) the
time of flight is found using the
equation for the vertical motion:
y = y
0
+ v
0
sin θ t – 1
2
gt
2
where y
o
is the initial height of the
ball and y is the position of the ball
when it hits the floor.