Bullet trajectories and Newton's Principia

[ja!mee]

Homework Statement

Newton's Principia suggested that if you fire a cannon from a high mountain it could fall, circle the earth, or fly away depending on how hard it was fired. Describe how this compares to bullet trajectories. What is the major difference with this trajectory? (for visualizing, see: http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/newt/newtmtn.html )

The Attempt at a Solution

Okay, with this problem I get that if you fire a cannon it could react this way , due to the fact the cannonball would a) succumb to gravity b) get caught betweens Earth's gravity field and begin to orbit or, C) would fly off into space in accordance to Newtons law of motion.

What I don't get is how this compares to bullet trajectory. As far as I understand this would be the same case for a bullet trajectory, with the only difference being F=ma. (please correct me if I am wrong here)

but as this is a kinematics section of a course, it seems that the force answer was not the correct one. Can anyone explain the similarities and differences in terms of kinematics, not force or circular motion (if possible) as I am struggling to grasp this in kinematic terms.

thanks in advance,

 

[Delphi51]

The force of gravity should have the same effect on the bullet as on the cannonball.

According to the picture, the cannon is always fired horizontally.
A bullet fired near the surface of the Earth usually is angled upward, even when aimed at a target at the same height. Could that be the "major difference"? Another factor is air resistance, much less up at mountain height.

 

[ja!mee]

hmm yes I think that may be part of it. I still just don't feel totally satisfied with that answer. I just feel as though something is missing. maybe I am just trying to complicate the matter.

 

[Delphi51]

Me, too. Another thing; the bullet from a gun is of lower speed than something that can go into an orbit, so its trajectory will be a parabola in contrast to the circle or ellipse of the orbiting cannonball.

 

[asteriatic]

I can provide some clarification on this topic. The major difference between the trajectory of a bullet and the trajectory of a cannonball fired from a high mountain is the initial velocity and the air resistance. When a bullet is fired from a gun, it has a much higher initial velocity compared to a cannonball fired from a high mountain. This higher initial velocity gives the bullet a flatter trajectory, meaning it will travel further before hitting the ground compared to the cannonball. Additionally, the bullet is smaller and more aerodynamic, so it experiences less air resistance, allowing it to maintain its velocity for a longer distance.

In terms of kinematics, the initial velocity and air resistance play a major role in determining the trajectory of an object. The initial velocity determines the speed and direction of the object, while air resistance affects the acceleration and deceleration of the object. Therefore, the major difference in bullet trajectories compared to the cannonball trajectory is the initial velocity and air resistance, which ultimately affect the shape and distance of the trajectory.

Furthermore, Newton's Principia also applies to the trajectory of a bullet. The same principles of gravity and motion govern the trajectory of a bullet as well. However, the difference lies in the initial conditions of the bullet's trajectory, which leads to a different shape and distance compared to the cannonball's trajectory.

In conclusion, while Newton's Principia applies to both bullet and cannonball trajectories, the major difference lies in the initial conditions and air resistance, which determine the shape and distance of the trajectory.