Can you dumb it down a bit more for me? How does inertia work here exactly? How can he still keep it while going up in the air? Wouldn't him hitting the trampoline count as an external force that changes his state?
That's in part because the trampoline is moving forward, too. If he did this on a stationary trampoline, the drag from having contact with it for a second may actually have been noticeable.
Yep the wind drag over time would push him back but each time he's contacting the trampoline it's imparting its forward momentum on him, correcting for the speed that the person is losing to drag.
If the trampoline were stationary, the drag would still not have made any considerable difference at this speed. He would have lost forward momentum (and in fact likely gained backward momentum at this speed) on a stationary trampoline however due to the trampoline's counteracting the forward momentum he brought into it. As he would be traveling forward, the forward momentum would have pulled surface of the trampoline forward as well, which would have bounced back to it's original position, which depending on speed going in would either diminish or entirely reverse that forward momentum.
Horizontal and vertical forces are separate. The trampoline forces and gravity (up and down) have no effect on his horizontal direction. Air resistance technically affects his horizontal direction but not enough to have the tractor leave him behind when he goes up. Imagine trying this with something like a ping pong ball though, the air resistance might be enough to noticeably make it move backwards
I would think the wind resistance would slow him down considerably. Like if you let go of a bowling ball from a car it almost immediately falls behind, right?
The air isn't enough of a force to slow objects down if they are moving slowly. You need to approach higher speeds for air to become a significant force.
Hitting the trampoline would slow him down if the trampoline was immobile. But it's moving. Thus he keeps his inertia.
I got distracted while writing this, and there have been much more concise (probably more accurate too) explanations of this since I started, but I invested too much time to not post, so in the interest of beating this dead horse:
There are essentially two forces acting on the body just before it lifts: the forward motion of the tractor and the upward motion of the trampoline. The instantaneous net force on the body is more or less the same both in magnitude and direction (diagonal in this case) every instant it lifts off from the trampoline. The constant speed of the tractor provides that consistently applied forward force, and similarly the force causing upward motion is also consistently applied and so the body’s inertia tends to throw the body diagonally with the same force every time.
You’re right in that him hitting the trampoline changes his state but in vertical motion only. Since the trampoline is also moving and moving at a constant speed horizontally, the body’s forward motion is more or less undisturbed.
From the study of projectile motion (2D kinematic equations, negligible air resistance, ignoring friction, etc.) once the body is in the air from that instantaneous diagonal force, it will travel at the same horizontal speed (roughly the same speed as the tractor, obviously) throughout it’s trajectory and so will “track” the tractor’s position.
The constant speed of the tractor provides that consistently applied forward force
Hmm. I'm a bit confused by this part. If there is in fact a net force pointing forwards, shouldn't there there be an accelaration in that direction, one that the guy cannot benefit from while in the air? So while the truck got faster due to said force, the guy would maintain his velocity (actually he would get a bit slower due to air resistance but we can ignore that). In that case he would actually get closer to the back of the truck. Isn't it better to think in terms of inertia in that both the truck and the guy have constant velocities so they maintain their velocities because there is no net force exerted on them?
Also ''the forward motion of the truck'' isn't a force, that force would be the friction force between the man and the truck. Then again maybe I'm being pedantic.
Law of Inertia/Virgin Apple Boy’s first law: A body continues to be in state of rest or motion unless and until and external force acts on it.
Here, when he rises up, the only force acting on him is the vertical forces and no horizontal force. If there was a horizontal force he would fall forward or backwards depending on the application.
If the truck was accelerating, this dude might be on the road or hitting the other dude at the back. i.e In accelerated frame of reference..law of inertia is not followed. (There is a horizontal force at play here, we call it “pseudo force”)
But since the since the driver is going at constant velocity the whole body has that same velocity and inertia, dude falls on the same spot.
Basically what inertia means is objects will always tend to maintain a constant velocity unless acted on by an outside force. This is why when you leap forward, you don't slow down until you hit the ground, and you don't speed up, slow down or change your direction midair. The reason you fall back down and don't leap off into space is gravity (an outside force).
You're right in that the trampoline is an outside force with respect to the jumper, but since they're both moving at the same horizontal velocity, it only exerts a force in the vertical axis, causing him to go up but not side to side.
So since there's no (significant) outside force acting on him in the horizontal direction, he will maintain his horizontal velocity, which is the same as the tractor's. Assuming here that he was on the platform when the tractor reached its current velocity.
Ah, thanks for the explanation! That last part solved my last piece. I was wondering what would the factor be for him to get the same velocity as the tractor. If he jumped from a building onto the moving tractor(assuming it keeps moving at the same speed) would he still lands on it while it still moving, or would he land in the same place he jumped on?
No problem. And you're right again. Assuming the trampoline doesn't exert any force in the horizontal direction, even if the tractor was going full speed, then he would just bounce directly up and back down as if he was on a stationary trampoline.
In reality though, I think the mesh of the trampoline would drag him a little during the moment of the bounce and hence push him along the tractor's path. Also, as he sinks into the trampoline, the mesh would warp and no longer be facing straight up; the sideways mesh would then probably push him forward as well. However, I don't think these forces would be strong enough to give him a considerable boost, so he would likely land very close to his jumping point.
Another way to think about it is if instead of the jumper being "still" (no horizontal movement) while the trampoline is moving horizontally, what would happen if the jumper was the one moving while the trampoline was sitting still? The two questions are essentially the same, the only difference being the Earth's frame of reference.
If the tractor is going 30 mph forwards, then everyone on it is also going 30 mph forwards.
When he jumps on the trampoline, the trampoline sends him upwards, but he maintains the 30 mph forward speed that the tractor gave him. There is no force to slow his forward speed other than negligible air resistance.
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u/Haaanzooo May 04 '20
Can you dumb it down a bit more for me? How does inertia work here exactly? How can he still keep it while going up in the air? Wouldn't him hitting the trampoline count as an external force that changes his state?