I have a Physics impaired friend
I’ve read the analogy countless times of how a cannon ball shot out of a cannon will hit
the ground at the same time as cannon ball dropped from the height of the firing
cannon’s muzzle. I grasp that the effect of gravity does not change for an object in motion (LAW) but, wouldn’t the amount of gunpowder and the trajectory of the cannon have major effects on countering the effects of gravity being placed on the ball or does this inference (like I believe to be the case) only work for a horizontal firing sequence?

I need some further evidence to prove a “Physics Impaired” friend wrong!

PeaceOut

This is only true of a cannon ball fired horizonally. And then, only for one that doesn’t go a tremendous distance, as the earth curves down.

The point is that if the cannon is fired horizontally, it applies no vertical force/acceleration/velocity. In that case, the cannon ball is essentially a body at rest in the vertical components of velocity and acceleration, and the acceleration of gravity affects the cannon ball in exactly the same way regardless of horizontal velocity or acceleration. On the other hand, if you point the cannon up at an angle, then the cannon does give it a vertical velocity, and it’s no longer comparable to a body at rest in the vertical components. This may take a little intuition to imagine, but it’s really simple to demonstrate if you take the basic equations of motion and separate the vertical and horizontal components.

All of which is a really long-winded way of saying Bill H. is right.

Trouble is, I think, there is no further evidence.

Your physics impaired friend just has to deal with this fact of life. Pointing out that moving very fast horizontally does not (contrary to the things we see in cartoons) slow down your movement vertically might be an option though, as it was for me.

If you aim the cannon at the point where the other cannonball is dropped from, the two cannonballs will always collide (ignoring air resistance and other details). The reason is the same: the two cannonballs will be equally subject to downward acceleration due to gravity.

What is it exactly that your friend thinks?

You want to really confuse him try and explain to him that when the shuttle (or anything else) is orbiting the Earth its the same thing, except that its horizontal speed is so great, even though its constantly ‘falling’ back to the Earth, the Earth constantly curves out from underneath it!

You can do this experiment to show that it’s true:

materials:
a tennis ball
a table
a stopwatch, or a video camera that can record a time index on the tape

Record the time it takes for the ball to fall when you:
Drop the tennis ball from the same height as the table.
Place the tennis ball on the table and gently roll it off the edge.
Repeat, but roll it more forcefully off the edge.
Repeat with even more force.

The times will all be the same.

There are two standard physics experiments here. The horizontal cannon is one of them, plenty about that above. The other one is the colliding/falling objects one, usually called the Monkey-in-a-Tree experiment, or the like. Demo

Since gravity acts on everything equally, if two objects are on a collision course w/o gravity, adding gravity still means they collide.
You do this by riggin up a tin can on an electromagnet on the ceiling, and a straight track where your projectile (a BB usually), will come from. Line up the track so it points at the can, and fire. As the BB leaves the track end, have it break the magnet circuit somehow. Both start reacting to gravity, and collide. (And, in one case, ricochet into my backpack where I find it that night. My favourite prof - two demos every day :D)

The last two words should be “pretty close.” When you do this experiment in air and the tennis ball is spinning, effects other than gravity get into the act.

A lot of these idealized experiments are only approximately correct when observed in the real world. Galileo supposedly figured out that objects fall at the same rate regardless of their mass. Try to tell me that a ping-pong ball and a golf ball fall at the same rate (outside a vaccuum).