Function if a plane dropping a bomb.

In summary, in the conversation, the speaker is trying to find the total distance a bomb will travel when dropped from a height of 8000m with an initial velocity of 0 and acceleration of -9.8. They mention using the free fall formula and finding a function for the movement of the bomb, represented as y=x. After some calculations, the speaker arrives at the function f(x)=-4.9x^2+8000. They then mention using the arc-length formula to find the total distance, but are unsure of how to find the function for a bomb being dropped with horizontal movement. The conversation ends with the speaker being given some values to use in the formula and asked to plug them in to find the function
  • #1
Metalsie
5
0
Vertically:
The initial velocity: =0
Acceleration: a=-9.8
Target Height: y=0
Current Height: y=8000m
time=40.40

Horizontally:
Velocity=133.88
Acceleration=0
time=40.40

Using these values, I have calculated that the bomb will drop 5408.75 meters away. Now I am trying to find the total distance the bomb travels when its dropping. In order to do that, I need a function for the movement of the missile.

How can I find that function? And by function I mean its representation in terms of y=x

Edit: I used the free fall formula and got

f(x)=-4.9x^2+8000

When I graph this, the curve doesn't even come close to 5000 on the x plane. Is there a way to show it from the perspective of someone on the ground?
 
Last edited:
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  • #2
To find the total distance the bomb travels, you can use the arc-length formula:

\(\displaystyle s=\int_a^b\sqrt{\left(\d{x}{t}\right)^2+\left(\d{y}{t}\right)^2}\,dt\)

Can you find the values you need for this formula?
 
  • #3
Yes that's the formula I'm trying to use. sqrt(1+(dx/dy)^2)

I need a function to derive first but I don't know how to get that function. I found ways to calculate the function that is launched from a cannon which goes up and down, a way to calculate the free fall function, but not a function where one is dropped with a horizontal movement.

View attachment 3788

It looks something like this. I need to find the function of this curve.
 

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  • #4
We are given:

\(\displaystyle a=0\)

\(\displaystyle b=40.4\)

\(\displaystyle \d{x}{t}=133.88\)

And we can infer:

\(\displaystyle \d{y}{t}=-9.8t\)

So, plug those in...what do you get?
 

FAQ: Function if a plane dropping a bomb.

How does the function of a plane dropping a bomb work?

The function of a plane dropping a bomb involves a series of steps. First, the pilot must identify the target and calculate the necessary altitude and speed for the bomb to hit its intended location. Then, the bomb is released from the bomb bay or bomb racks of the plane. Depending on the type of bomb, it may be guided by a laser or GPS system to ensure accuracy. Finally, the bomb detonates upon impact with the ground, causing destruction to the target area.

What types of bombs can be dropped from a plane?

There are various types of bombs that can be dropped from a plane, including gravity bombs, guided bombs, and cluster bombs. Gravity bombs are simply dropped from the plane and rely on gravity to guide them to the target. Guided bombs use sophisticated technology, such as lasers or GPS, to ensure accuracy. Cluster bombs contain multiple small explosive submunitions that disperse over a large area upon detonation.

How accurate are bombs dropped from a plane?

The accuracy of bombs dropped from a plane depends on various factors, such as the type of bomb, weather conditions, and the skill of the pilot. Guided bombs have a higher level of accuracy due to their advanced technology. However, even gravity bombs can be accurate if the pilot has properly calculated the necessary altitude and speed for the bomb to hit its intended target.

Can a plane drop multiple bombs at once?

Yes, a plane can drop multiple bombs at once. This is often done when targeting a larger area or multiple targets. Some planes are equipped with multiple bomb racks, allowing them to drop multiple bombs simultaneously. Additionally, guided bombs can be released in a cluster, increasing the chances of hitting the intended target.

What precautions are taken to ensure the safety of the plane and pilot when dropping a bomb?

When dropping a bomb, pilots must follow strict protocols to ensure their safety and the safety of the plane. This may include flying at a certain altitude and speed, avoiding potential hazards, and communicating with other aircraft in the area. Additionally, planes may have defensive measures, such as flares or chaff, to protect against enemy attacks. Pilots also undergo extensive training to handle emergency situations and minimize risks during bomb drops.

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