Formula of projectile range with mass consideration
Answers
As pointed out by Rajendra Meena, the question should be “Why range of a projectile is independent of its mass?”. So, I will answer that.
Actually, it is true when one neglects the air resistance.
How far the projectile travels depends on (i.e. product of) its horizontal velocity and the time for which it remains airborne.
Now, horizontal velocity remains the constant as there is no force acting on horizontal direction. (Newton’s First Law)
Going for the time interval. It depends on the initial vertical velocity (let it be ‘v’) and acceleration due to gravity (let it be ‘g’) as time t=2v/g (Using the simple kinematics equation, v=u+at)
As both of them as independent of mass, so the time interval is also independent of mass of the projectile.
All of this resulting in the range of projectile being independent of its mass.
BUT only if you neglect air resistance.
If we consider air resistance also, you get an extra drag force depending on the velocity (directly proportional to velocity or square of velocity) acting upon the projectile in direction opposite to its velocity.
So, now extra acceleration along vertical and horizontal comes to be inversely proportional to its mass.
So, horizontal velocity changes and the change depends on its mass, and time depends on mass as vertical acceleration is dependent on mass.
If you workout the equation, you will find that the mass parameter shows up in the range equation.
The first step is to separate the problem into two sets. Use one of the kinematic equations (dependent on what information you are given) to find how long it would take for the projectile to fall to the ground from the height you are provided with. This time then can be used in a kinematic equation you choose to find how far the projectile will travel in the x direction in said time.
(Keep in mind that this only works when ignoring air resistance. To associate non-conservative forces, much more work will be necessary.)
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A basic rule of thumb when firing a projectile. Common sense says that if you fire at a 45* angle then you achieve maximum range. That is not true and you actually achieve maximum range at an angle close to 48* barrel elevation. That is because the projectile is spinning and gains a little height from that when traveling through the air. There are other variables concerning accuracy but that is the is the main one for range.
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consider the original amount of force used in the projectile. how much the projectile weights. the gravity against the the projectile the wind in the matter also the humidity on that day. if you have more questions in this matter feel free to email me