# Math Help - at what pint wood a missile hit?

1. ## at what pint wood a missile hit?

hi look for some help with this plz

i have 2 ship in space, one is movering at 175 m/s the over is movering 170m/s, there are 45 km betreen them. the faster one is at the back and fire a missile at the over one
max flight time = 10.00s max velocity = 3750m/sec.

what i wood like to no is wen wood my missile hit the over ship?

2. Originally Posted by Kayron
hi look for some help with this plz

i have 2 ship in space, one is movering at 175 m/s the over is movering 170m/s, there are 45 km betreen them. the faster one is at the back and fire a missile at the over one
max flight time = 10.00s max velocity = 3750m/sec.

what i wood like to no is wen wood my missile hit the over ship?
Why do you think it would ever hit?

(Also your question is poorly formulated, why in space is there a maximum time of flight, also the max velocity is with respect to the instantaneous rest frame of the firing ship at launch. We are at low speeds so Galilean relativity is useable, ...)

CB

3. Originally Posted by Kayron
hi! looking for some help with this plz,

I have 2 ships in space, one is moving at 175 m/s, the over is moving at 170m/s, there is 45 km between them. The faster one is at the back and fires a missile at the other one.

max flight time = 10.00s, max velocity = 3750m/sec.

what i would like to know is when would my missile hit the other ship?
Omitting numerous practicalities of space-flight and change of speed of the missile,
modelling the situation in a basic linear way...

Taking max flight time as the time within which the missile needs to strike....
If the faster ship is following directly behind the other in a straight line,
then when the missile is fired, it's gaining on the ship in front at

3,750-170 meters per second

which is 3,580 m/s...which is the speed of the missile "relative to" the target.
(You can imagine the target "frozen" in space if you want).

There is a 45km distance to traverse (if you imagine the ship stopped and the missile travelling at "relative" speed)

$\frac{45,000}{3,580}>10$

It'll take more than 10 seconds.
Is the missile still dangerous after 10 seconds?

4. The problem is not so trivial as it seems at first!... the missile is traveling in the vacuum so that once it uses up the fuel, it mantains the reached speed. In order to impost the problem we indicate with ...

a) $s$ the propulsion of the missile while the fuel burns [that we suppose constant...]

b) $m_{0}$ the mass of the missile without fuel...

c) $m_{f}$ the mass of the fuel...

d) $t_{0}$ the time in which the fuel is off [10 seconds...]

e) $v_{0}$ the speed of the missile at the time $t_{0}$ [3750 m/s...]

The speed of the missile obeys to the DE...

$\displaystyle v^{'} = \frac{s}{m_{0} + m_{f} (1-\frac{t}{t_{0}})} , v(0)=0$ (1)

... and its solution is...

$\displaystyle v(t)= - \frac{s} {m_{f}}\ \ln (1-\frac{m_{f}}{m_{0} + m_{f}}\ \frac{t}{t_{0}})$ (2)

At this point we have three unknown parameters [ $s$, $m_{0}$ and $m_{f}$...] and only two known parameters [ $t_{0}$ and $v_{0}$ ...] , so that we can't proceed without further information. The only that we can calclude is that the missiles will hit the target in a time t < 9000 seconds...

Kind regards

$\chi$ $\sigma$

5. Originally Posted by Archie Meade
Omitting numerous practicalities of space-flight and change of speed of the missile,
modelling the situation in a basic linear way...

Taking max flight time as the time within which the missile needs to strike....
If the faster ship is following directly behind the other in a straight line,
then when the missile is fired, it's gaining on the ship in front at

3,750-170 meters per second

which is 3,580 m/s...which is the speed of the missile "relative to" the target.
(You can imagine the target "frozen" in space if you want).

There is a 45km distance to traverse (if you imagine the ship stopped and the missile travelling at "relative" speed)

$\frac{45,000}{3,580}>10$

It'll take more than 10 seconds.
Is the missile still dangerous after 10 seconds?
ok then i fire one off at 45km i wate some time say 4mis i fire agen ans so on
what pint in km from the ship wood they hit the over one?

6. Originally Posted by Kayron
ok then, I fire one off at 45km behind the target, I wait some time... say 4mins, I fire again and so on...
At what point (in km from the leading ship) would they hit the other one?

Are we just assuming the missile can continue tracking the target at max speed,
until it's gone beyond it's lethal range after 10 seconds ?

7. Originally Posted by Kayron
ok then i fire one off at 45km i wate some time say 4mis i fire agen ans so on
what pint in km from the ship wood they hit the over one?
Tell us about the context for this question so we can make sensible comments, as it is it looks like badly thought out nonsense.

If it is homework post the exact question .

CB