Why does a projectile follow the same trajectory no matter what its size is?

Question

For example, a soccer ball and a tennis ball and a marble were all launched at 12.8m/s horizontally. How come the trajectory of the projectile is the same for all these objects?

Answer 1

We neglect air resistance, of course. The gravitation force vector F (pulling it downward) is proportional to the ball's inertia (aka mass m, tending to preserve its speed an direction), so m cancels out of the equation of motion (downward acceleration = F/m).

Answer 2

What you are suggesting is true only in a vacuum.

The reason for the sameness in a vacuum is because the forces acting on both balls cause their horizontal and vertical velocities to be the same during flight. (You failed to specify that the vertical velocities were the same. If they were not, their trajectories would differ.)

The vertical forces in flight are their respective weights. Weight is W = mg; so that g = W/m which is 9.81 m/sec^2 for both bodies because g is a constant acceleration due to gravity at the Earth's surface.

From the moment a ball leaves the launch mechanism (e.g., your hand), the weight of the ball begins to slow it down until it reaches zero vertical velocity. The point where the vertical velocity reaches zero is Vf = Vi - gt = 0; so that Vi = gt and t = Vi/g

Note the time ascending does not depend on the masses of the bodies...only on the initial vertical velocities. Also note the minus sign for gt shows the gravitational pull is in a direction opposite to the direction of the velocity.

This is why we must assume the vertical velocities of the two balls are the same. Otherwise, one would be in the air a different length of time (t) As what goes up must come down, total time in the air is 2t = tup + tdown and the times up and down are identical since g = constant.

As to the horizontal segment of the trajectory, in a vacuum, there are no horizontal forces acting on a projectile after launch. Thus, in a vacuum, the projectile will stay moving at its initial horizontal velocity (e.g., Hi = Hf = 12.8 m/s) until it impacts the ground. You can find how far each ball will travel horizontally before it impacts by Sh = H X 2t; where t is the time up or down and H = 12.8 m/s.

Answer 3

No. I do not think it will be same. What we are not considering is the air resistance and the drag experienced by these different projectiles. When we consider the drag the trajectories will be different for each of these projectiles. In this case all of these trajectories will be distorted parabolas. The range will be maximum for marble and least for the soccer ball. The trajectory will be a distorted and not a symmetrical parabolas due to air resistance as stated earlier.

Answer 4

So a horizontal projection the only thing influencing their path is force acting on the balls due to gravity.

As they are all of roughly the same shape we can pretty much ignore air resistance.

The acceleration due to gravity is the same for all objects, no matter what the size.

Answer 5

the direction which the particle follows relies upon on the character of the rigidity. grav and magazine forces have diverse rigidity rules. once you're deriving the above equations you're assuming that the direction of the gravitational rigidity is continuous (and likewise its magnitude) that's definitely in basic terms an approximation. when you consider that this sort of rigidity produces parabolic trajectories, thats what u r getting. in extremely if u learn the direction observed by using a real merchandise you will discover that it isn't a parabola, yet an element to a spiral. newtons gravitation rigidity regulation is the properly suited regulation to apply which produces spirals in such cases.

Answer 6

I think part of it is because they are all the same shape. Did the size and weight affect the distance that they traveled?

Answer 7

Because gravity accelerates all objects at the same rate.

Answer 8

Ideally, or course there will not be any difference.Practically speaking though, air resistance will play a role on their path.