User's Manual

®
Model No. ME-6830 Exp. 12 (Demo): Shooting Through Hoops
012-05375C 47
Exp. 12 (Demo): Shooting Through Hoops
Equipment Needed
Purpose
The purpose of this demonstration is to confirm that the part of a projectile is parabolic.
Theory
The range is the horizontal distance, x, between the muzzle of a Launcher and the place where the projectile hits,
given by:
where v
0
is the initial speed of the projectile as it leaves the muzzle and t is the time of flight. The vertical position,
y, of the projectile at time t is given by:
where y
0
is the initial height of the projectile and g is the acceleration due to gravity.
Solving the x-equation for t and substituting the expression in the y-equation gives:
where “a” and “b” are constants. The y-equation (y = ax
2
+b) describes a parabola.
Pre-Lab
Before the demonstration begins, find the initial speed of the bal. Use two photogates and a photogate mounting
bracket with a PASCO Interface or Timer or shoot the ball horizontally and measure x and y. (Use y to calculate the
time of flight. See experiments 1 and 2.)
Setup
1. Clamp the Projectile Launcher to a sturdy table near one end of the table with the Launchers aimed away from
the table so the balls will land on the floor.
2. Adjust the angle of the Launcher to 0° so the balls will fire horizontally.
Procedure
1. Measure and record the initial height, y
0
, of the ball at muzzle level.
Item Item
Projectile Launcher and plastic ball Ring clamp on stand (5)
Photogate Head ME-9498A (2) optional Photogate Mounting Bracket ME-6821A optional
Meter stick Two-meter stick
xv
0
t=
yy
0
1
2
---


– gt
2
=
yy
0
1
2
---


– g
x
v
0
-----


2
ax
2
b+==