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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?Quote:
Originally Posted by Kayron
(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
Omitting numerous practicalities of space-flight and change of speed of the missile,Quote:
Originally Posted by Kayron
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)
$\displaystyle \frac{45,000}{3,580}>10$
It'll take more than 10 seconds.
Is the missile still dangerous after 10 seconds?
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) $\displaystyle s$ the propulsion of the missile while the fuel burns [that we suppose constant...]
b) $\displaystyle m_{0}$ the mass of the missile without fuel...
c) $\displaystyle m_{f}$ the mass of the fuel...
d) $\displaystyle t_{0}$ the time in which the fuel is off [10 seconds...]
e) $\displaystyle v_{0}$ the speed of the missile at the time $\displaystyle t_{0}$ [3750 m/s...]
The speed of the missile obeys to the DE...
$\displaystyle \displaystyle v^{'} = \frac{s}{m_{0} + m_{f} (1-\frac{t}{t_{0}})} , v(0)=0$ (1)
... and its solution is...
$\displaystyle \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 [$\displaystyle s$, $\displaystyle m_{0}$ and $\displaystyle m_{f}$...] and only two known parameters [$\displaystyle t_{0}$ and $\displaystyle v_{0}$ ...] , 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
$\displaystyle \chi$ $\displaystyle \sigma$
ok then i fire one off at 45km i wate some time say 4mis i fire agen ans so onQuote:
Originally Posted by Archie Meade
what pint in km from the ship wood they hit the over one?
Quote:
Originally Posted by Kayron
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 ?
Tell us about the context for this question so we can make sensible comments, as it is it looks like badly thought out nonsense.Quote:
Originally Posted by Kayron
If it is homework post the exact question .
CB
