Moose, you don't need to have a slingshot and speed up the test at all. The main factor in all of this is momentum. I posted the following in your other thread, but I thought that I'd post it here as well.
This is how I would go about it:
1. Figure out how fast the object is moving when dropped from 15 feet. This can be done with the known acceleration due to gravity (32.2 ft/s^2). This is the average acceleration across the Earth's surface. If you wanted a more accurate number, you'd have to factor in your elevation. This won't be necessary or matter for this purpose, unless you're at the summit of Mt. Everest or something. Anyway, the formula for the velocity of a free-falling object on Earth given a certain height is as follows:
v = sqrt(2*g*d)
v = sqrt (2 * 32.2 ft/s^2 * 15 ft)
v = 31.08 ft/s = 21.19 mph
2. Given the velocity of the object in your experiment, the desired velocity, and the desired weight, you can set up an equation of momentum. The main principle here is that you desire a momentum produced by a 15 lb object going 67 mph. Momentum is equal to the product of mass and velocity (p = m*v). Since you're looking to recreate the momentum from the desired experiment and you cannot change the velocity, you have to add mass. That gives you the following equation:
m1v1 = m2v2
(15 lb)*(67 mph) = (X lb)*(21.19 mph)
X = 47.43 lbs
3. So, for your experiment to produce the required momentum, your total weight needs to be 47.43 ~ 47.5 pounds. You currently have a 15 lb mass so therefore, you need to add an extra 32.5 lbs of mass to your weight.
4. Just as a note, there are some inaccuracies in this experiment. The calculations I made were using point-masses, not actual objects. The difference is not very large at all and will be negligable in what you're trying to accomplish. I would not worry about those. I figure that if air resistance isn't necessary, then it isn't necessary to dive into the center of mass/inertia values for the mass.
Hope this helps!
