How can assumptions impact the calculation of projectile and explosion?

In summary, a shell with a muzzle velocity of 600 m/s and an angle of 30.0o explodes into two equal fragments after 41.0 seconds. Fragment A falls vertically and Fragment B continues in the forward direction. To determine the distance Fragment B lands from the gun, certain assumptions must be made. These include the conservation of energy, instantaneous explosion, no air resistance, level terrain, a flat earth, and constant gravitational acceleration. The answer would change if any of these assumptions were not true. Therefore, it is necessary to assume 2, 3, 4, 5, and 6 to accurately determine the landing distance of Fragment B.
  • #1
amcavoy
665
0
A shell is fired from a gun with a muzzle velocity of 600 m/s at an angle of 30.0o with the horizontal. The shell explodes into two fragments of equal mass 41.0 s after leaving the gun. Fragment A, whose speed immediately after the explosion is zero, falls vertically. Fragment B proceeds in the forward direction. How far from the gun does fragment B land? What additional assumptions are needed to answer this question?:

1. energy is conserved
2. Instantaneous explosion
3. No air resistance
4. Level terrain
5. Flat earth
6. Constant g

I got the answer to the first part (35,374.04 m), but I'm having trouble with the second. At first, I thought 1,2,3,6 would be the answer, but that was wrong. Then, I said that 2,3,6 would be the answer, but that too was wrong. Now I am thinking that the energy wouldn't matter (momentum, however, would matter). 2 definitely needs to be assumed, as well as 3,4,5, and 6. The answer would change if there was air resistance, the terrain wasn't level (which would in turn that the Earth isn't flat), and finally if g was taken to be universal gravity rather than local, the answer would change a bit. Would I be correct to assume 2,3,4,5,6?

Thank you.
 
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  • #2
This question is sort of vague. 4 and 5 would basically be the same (at least in this context).
 
  • #3
If 4 and 5 are the same then your answer is correct.
In an explosion energy isn't conserved cause of the explosion, when you trigger the explosion then you change the energy:
if there is a bomb at rest then its energy is 0. But when it explodes it has a lot of kinetic energy.
 

Related to How can assumptions impact the calculation of projectile and explosion?

1. What is a projectile?

A projectile is any object that is thrown, launched, or fired into the air and is subject to the forces of gravity and air resistance. Common examples of projectiles include bullets, arrows, and baseballs.

2. What factors affect the trajectory of a projectile?

The trajectory of a projectile is affected by its initial velocity, angle of launch, and the forces acting upon it, such as gravity and air resistance. Other factors such as wind speed and direction may also play a role.

3. How is the range of a projectile calculated?

The range of a projectile is the horizontal distance it travels before hitting the ground. It can be calculated using the formula: range = (initial velocity² * sin(2*launch angle)) / gravitational acceleration. This formula assumes a flat surface and no air resistance.

4. What is an explosion?

An explosion is a rapid and violent release of energy from a confined space, resulting in the sudden expansion of gases and a loud noise. Explosions can be caused by chemical reactions, nuclear reactions, or mechanical means.

5. How are explosions studied and analyzed by scientists?

Scientists study explosions through experiments, computer simulations, and mathematical models. They use instruments such as high-speed cameras, pressure sensors, and acoustic sensors to measure and analyze the characteristics of explosions, such as the velocity of shock waves and the amount of energy released.

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