PASCO ME-6825A MINI LAUNCHER - Manual (Page 17)

012-05479B Mini Launcher
15
®
Experiment 3: Projectile Range Versus Angle
θ
x
v
0
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 horizon-
tal, 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 q - gt
peak
Therefore, solving for the time gives the total time of flight as t = 2t
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 q t - 12 gt 2
Figure 3.1: Shooting on a level surface