PASCO ME-6831 Ballistic Pendulum_Projectile Launcher - Manual (Page 15)

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M o d e l N o . M E - 6 8 3 0 E x p . 1 : P r o j e c t i l e M o t i o n
0 1 2 - 0 5 3 7 5 C 11
Exp. 1: Projectile Motion
Equipment Needed
Purpose
The purpose of this experiment is to predict and verify the range of a ball launched at an angle. The initial speed of
the ball is determined by shooting it horizontally and measuring the range of the ball and the height of the
Launcher.
Theory
To predict where a ball will land on the floor when it is shot from the Launcher at some angle above the horizontal,
it is first necessary to determine the initial speed (muzzle velocity) of the ball. That can be determined by shooting
the ball horizontally from the Launcher and measuring the vertical and horizontal distances that the ball travels.
The initial speed can be used to calculate where the ball will land when the ball is shot at an angle above the hori-
zontal.
• NOTE: For rest results, see the notes on “Repeatable Results” in the Introduction.
Initial Horizontal Speed
For a ball shot horizontally with an initial speed, v
0
, the horizontal distance travelled by the ball is given by x = v
0
t,
where t is the time the ball is in the air. (Neglect air friction.)
The vertical distance of the ball is the distance it drops in time t given by:
The initial speed can by determined by measuring x and y. The time of flight, t, of the ball can be found using
and the initial horizontal speed can be found using .
Initial Speed at an Angle
To predict the horizontal range, x, of a ball shot with an initial speed, v
0
, at an angle,
, above the horizontal, first
predict the time of flight from the equation for the vertical motion:
where y
0
is the initial height of the ball and y is the position of the ball when it hits the floor. In other words, solve
the quadratic equation for t and then use x = v
0
cos

t where v
0
cos

is the horizontal component of the initial
speed.
Setup
1. Put the Launcher in the top position on the Ballistic Pendulum upright. Clamp the Ballistic Pendulum/Projec-
tile Launcher to a sturdy table or other horizontal surface. Mount the Launcher near one end of the table and
aimed away from the table.
Item Item
Projectile Launcher and plastic ball Plumb bob and string
Meter stick Carbon paper
White paper Sticky tape
y
1
2
---gt
2
=
t
2y
g
------ =
v
0
x
t
-- =
y y
0
v
0

sin
 t 1
2
---gt
2
– + =