Solving Missile Attack with Anti-Missile: What Velocity is Needed?

[Tappen]

Hello everyone, new here and looking for some help, really don't know where to start with this one and could use all help possible, thanks for your time.

Homework Statement

terrorists using a .5 megaton nuclear missile shoot it at my town, it must be destroyed at least 3km away(radius). We make an anti missile 2km away from my town right on path with the nuke. our launcher can fire our rocket at a maximum of 280 m/s(initial velocity and no propulsion)

Our defence network detects launch at 9:00 am, and measures initial velocity of the object as 1470km/h (76.25 degrees up) it has no propulsion and is on target.

The question is, what velocity will our rocket stop the missile, and how long after the missile launch must we launch or rocket to stop it.

Homework Equations

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no relevant equations

The Attempt at a Solution

No idea where to start.

 

[anathema]

Hello and welcome to the forum! I can understand your concern and desire for help in this situation. Let's break down the problem and see if we can come up with a solution.

First, we need to determine the distance between the anti-missile launcher and the town. You mentioned that the launcher will be 2km away from the town, but we also need to consider the distance between the launcher and the missile's trajectory. This will give us the total distance that the rocket needs to travel to intercept the missile.

Next, we need to consider the speed and direction of the missile. You mentioned that it has an initial velocity of 1470km/h and is on target. We also know that it will be 3km away from the town when it explodes. Using this information, we can calculate the time it will take for the missile to reach the town.

Now, let's look at the capabilities of our anti-missile launcher. You mentioned that it can fire a rocket at a maximum velocity of 280 m/s. We need to determine the minimum velocity that the rocket needs to have in order to stop the missile. This will depend on the distance between the launcher and the missile's trajectory, as well as the time it takes for the missile to reach the town.

Finally, we can calculate the time delay between the launch of the missile and the launch of our rocket. This will depend on the time it takes for the missile to reach the town, as well as the time it takes for our rocket to reach the missile.

I hope this helps you get started on solving the problem. Let me know if you have any further questions or need clarification on any of the steps. Good luck!