A rocket that explodes not on impact, but explodes on a timer will be shot from myself to the enemy. The timer can only be inputted at the start of the shot. The rocket can only go straight and has a speed of 1500m/s . The enemy is moving away from me in a straight line at a speed of 400m/s. The distance between myself and my enemy is 5000m. I need a formula that predicts the precise time until the rocket should explode so that it will explode directly on my enemy's location.
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Do you know which direction your enemy is traveling? Are they coming towards you, away or at some fixed angle? – AHusain Sep 30 '18 at 18:31
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Find values of the time $t$ for which the target lies on the circle with radius $1500t$ centered on the rocket’s launch point. – amd Sep 30 '18 at 18:54
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@AHusain Away from me. – Gwapo Sep 30 '18 at 22:15
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If they are going directly away from you, the problem is only one dimensional. Let us put you at $x=0$. Your enemy starts off at $x=5000$.
Your enemies position as a function of time is
$$ x_{enemy}=5000+400t $$
The rocket's position as a function of time is
$$ x_{rocket}=0+1500t $$
Set $x_{enemy}=x_{rocket}$ and solve for the $t$ at which they meet.
$$ 5000+400t=1500t\\ 5000+400t-400t=1500t-400t\\ 5000=1100t\\ \frac{5000}{1100}=\frac{1100t}{1100}\\ \frac{50}{11} = t\\ $$
It takes $\frac{50}{11}=4\frac{6}{11}$ seconds.
AHusain
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Could you also mention just in case if they were moving at an angle either going nearer or further away from me, what the changes to the formula would be. Thank you. – Gwapo Oct 01 '18 at 10:32