# Find the place of the explosion

• user5
In summary, the conversation discusses the use of friction force in finding the coordinates of an explosion. The friction force is only considered in the horizontal equation and not in the vertical equation. The correct equation for the vertical equation should be y'' + ky + g = 0, where the friction force is opposite to the velocity. The standard method for solving this equation involves factoring and finding the solutions using the variables a and b.
user5
A missile is fired at speed V0 at an angle 450. The missile exploded into two parts when reaches the maximum height. The part of mass m1 is thrown back at speed V1 relative to the missile speed before the explosion (V1>V0). From the shot till the explosion the wind was blown that exerts a friction force Ffriction =−kV. Exactly at the explosion the wind stops to blow. Find where the explosion accrues.

Why in finding the y cordinate there is no use of the friction force? the answer says: yexplosion=V0sin45∗texplosion−0.5∗g∗t2explosion while in finding the x coordinate there is a use, didn't friction have to be taken into consideration in both coordinates? Does friction force is only horizontal and not opposite the direction of the velocity?

hi user5!
user5 said:
From the shot till the explosion the wind was blown that exerts a friction force Ffriction =−kV.

Why in finding the y cordinate there is no use of the friction force? the answer says: yexplosion=V0sin45∗texplosion−0.5∗g∗t2explosion while in finding the x coordinate there is a use, didn't friction have to be taken into consideration in both coordinates?

yes, i think you're right, and that equation is wrong

the friction seems to be opposite to the velocity,

so the governing vertical equation should be y'' + ky + g = 0

1 person
thank you very much!
may you help me with solving this equation?

hi user5!

there's a standard method, which is to write d/dx = D, making it:

(D2 + kD + g)y = 0​

you then factor that to (D - a)(D - b)y = 0

and the solutions are:

y = C1eax + C2ebx if a ≠ b

y = (C1 + C2x)eax if a = b

I would first clarify that the given information is not enough to accurately determine the exact location of the explosion. However, based on the given information, we can make some assumptions and provide a response.

Firstly, it is important to note that the friction force in this scenario is only acting horizontally and not in the opposite direction of the velocity. This is because the wind is blowing in the same direction as the velocity of the missile, therefore, the friction force will only act in the direction opposite to the wind's direction.

In terms of finding the y-coordinate of the explosion, we do not need to take into consideration the friction force because it is acting horizontally and does not affect the vertical motion of the missile. Therefore, the equation for the y-coordinate only includes the initial velocity, the angle of launch, and the acceleration due to gravity.

On the other hand, in finding the x-coordinate, we do need to take into consideration the friction force because it affects the horizontal motion of the missile. The equation for the x-coordinate includes the initial velocity, the angle of launch, the acceleration due to gravity, and the friction force.

In conclusion, the friction force is only acting horizontally and does not affect the vertical motion of the missile. Therefore, it is not included in the equation for the y-coordinate of the explosion. However, it does affect the horizontal motion, and hence, it is included in the equation for the x-coordinate.

## What is the purpose of finding the place of the explosion?

The purpose of finding the place of the explosion is to determine the exact location where the explosion occurred. This information can be used to investigate the cause of the explosion and prevent similar incidents from happening in the future.

## How is the place of the explosion determined?

The place of the explosion is determined by analyzing various factors such as eyewitness accounts, debris patterns, and blast marks. Investigators may also use forensic techniques and technology to pinpoint the exact location of the explosion.

## Why is it important to find the place of the explosion quickly?

It is important to find the place of the explosion quickly in order to secure the area and prevent any further potential dangers. It also allows investigators to collect evidence before it is disturbed or destroyed.

## What types of explosions can be investigated?

Any type of explosion, such as industrial accidents, gas leaks, or terrorist attacks, can be investigated to determine the place of the explosion.

## What are the potential consequences of not finding the place of the explosion?

Not finding the place of the explosion can hinder the investigation and make it difficult to determine the cause of the explosion. This can also delay any necessary safety measures and prevent justice for those affected by the explosion.

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