Calculating Velocity, Range & Height of a 2kg Projectile & Counterweight

In summary, the teacher's equation was not accurate and the student attempted to solve the problem himself by using conservation of energy. However, he needed a working equation that would give him the initial velocity, range, and maximum height of the projectile.
  • #1
>>>SiM>>>
2
0

Homework Statement



Example:

2 kg projectile
2 kg Counterweight
Dropped from 1m
45 Degree Angle
9.8 m/s Gravitational Acceleration

(For a catapult)

Homework Equations



My science teacher's equation was blatantly wrong in a number of ways, so I no longer have it.

The Attempt at a Solution



When I use his formula, not only does the velocity come out wrong, but the range is completely inaccurate, especially when the Gravitational Acceleration is altered. For example, changing the Gravitational Acceleration up or down seems to make the projectile go faster and farther, which makes no sense to me, since making it bigger should make it's distance less. Changing the Gravitational Acceleration to a negative number gives a negative answer which is wrong as well.

What I need to know is a working formula that will calculate the velocity, range, and maximum height of a projectile fired with the given five values (Mass of Projectile, Mass of Counterweight, Height the counterweight is dropped, Gravitational Acceleration, and Angle of launch). I attempted to find an answer on the internet, but then got confused trying to piece together the different formulas to fit my needs. If I have the formula, I intend to figure out the answers to all the questions myself.

He isn't available for contact so I can't ask him for a working formula myself, and I can imagine how frustrated my classmates are. My friend asked me to tell him as soon as I get an answer.
 
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  • #2
Please be more precise on your problem specification, its quite ambiguous.
 
  • #3
lzkelley said:
Please be more precise on your problem specification, its quite ambiguous.

I need a formula which will calculate the initial velocity of the projectile (m/s), the range of the projectile (meters) and the maximum height the projectile will reach (meters) using the Mass of the Projectile and Counterweight (kg), the height from which the counterweight is dropped (meters), the Angle it was fired (degrees), and the Gravitational Acceleration (m/s).
 
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  • #4
The only way to solve the situation with the given information is to use conservation of energy (which won't give a very accurate result).
Assume that the potential energy of the counterweight is completely converted to kinetic energy of the projectile. Groovy?
 

FAQ: Calculating Velocity, Range & Height of a 2kg Projectile & Counterweight

1. How do I calculate the velocity of a 2kg projectile?

To calculate the velocity of a 2kg projectile, you will need to know the mass, acceleration, and distance traveled. The formula for velocity is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. You can determine the acceleration from the force applied to the projectile and the mass of the projectile. Once you have all the necessary values, plug them into the formula to calculate the velocity.

2. What is the range of a 2kg projectile?

The range of a projectile refers to the horizontal distance it travels from its initial position to the point where it hits the ground. To calculate the range of a 2kg projectile, you will need to know its initial velocity, angle of launch, and height of the launch point. The formula for range is R = (v^2sin2θ)/g, where R is the range, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity. Plug in the values and solve for R to determine the range of the projectile.

3. How do I calculate the height reached by a 2kg projectile?

To calculate the height reached by a 2kg projectile, you will need to know its initial velocity, angle of launch, and initial height. The formula for maximum height is h = (v^2sin^2θ)/(2g), where h is the maximum height, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity. Plug in the values and solve for h to determine the height reached by the projectile.

4. What is the counterweight used for in this calculation?

The counterweight is used to balance the projectile and ensure that it reaches its intended target. It is typically a weight that is attached to the opposite end of the projectile launcher and is used to counteract the weight of the projectile. By adjusting the counterweight, you can control the trajectory and distance of the projectile.

5. Can these calculations be used for projectiles of different masses?

Yes, these calculations can be used for projectiles of different masses as long as the initial conditions, such as initial velocity and angle of launch, are the same. The formulas for velocity, range, and height are all dependent on the initial conditions and do not depend on the mass of the projectile.

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