Triggering a 12 volt relay

I have completed the mechanical design of a reactive target for pistol matches, but I just beginning to learn how to code for Arduino. At this point, I'm not even sure what I need to accomplish is possible, because it will require the resetting of a relay while the triggering circuit is still complete. Below is the events sequence I need to accomplish.

  1. When target is struck: Micro switch closes and the circuit triggers a relay for 1.5 to 2 seconds allowing the target to fall;
  2. Target falls: Micro switch may stay closed, or it may open (depending upon physical factors), but relay circuit needs to be de-energized;
  3. Target is manually raised to shooting position for next shooter, thus opening the micro switch/relay circuit;
  4. Opening the micro switch causes the Arduino to reset so that the relay circuit will be energized the next time the target is hit causing the micro switch close and energize the relay circuit.

I hope this description of the sequence of events makes sense. Is it possible to have the Arduino de-energize the relay circuit even when the trigger circuit is complete, then reset for the next cycle when the micro switch opens?

Thanks folks, Chas.

I should be quite straightforward. The pseudo code would look something like this:

loop() {
    If ( microswitch contacts closed now and were open last loop iteration ) {
         start timer
    If ( timer expiry 1.5 seconds not reached ) {
         relay on
    else {
         relay off