# Dynamics: Systems of Particles. Airplane and Helicopter collision find final position

1. Mar 17, 2012

### jaredogden

1. The problem statement, all variables and given/known data

The problem I must complete is problem 14.18

14.17 A small airplane of mass 1500 kg and a helicopter of mass 3000 kg
flying at an altitude of 1200 m are observed to collide directly
above a tower located at O in a wooded area. Four minutes earlier
the helicopter had been sighted 8.4 km due west of the tower and
the airplane 16 km west and 12 km north of the tower. As a result
of the collision the helicopter was split into two pieces, H1 and H2,
of mass m1 5 1000 kg and m2 5 2000 kg, respectively; the airplane
remained in one piece as it fell to the ground. Knowing that the
two fragments of the helicopter were located at points H1 (500 m,
2100 m) and H2 (600 m, 2500 m), respectively, and assuming
that all pieces hit the ground at the same time, determine the
coordinates of the point A where the wreckage of the airplane will
be found.

14.18 In Problem 14.17, knowing that the wreckage of the small airplane
was found at point A (1200 m, 80 m) and the 1000-kg fragment
of the helicopter at point H1 (400 m, 2200 m), and assuming that
all pieces hit the ground at the same time, determine the coordinates
of the point H2 where the other fragment of the helicopter
will be found.

2. Relevant equations

mr = mrG
mava + mbvb = mav'a + mbv'b

3. The attempt at a solution

I have been racking my brain for hrs on this one.. All I have done so far is find that the velocity of the helicopter is 35 m/s and the velocity of the airplane is 83.33 m/s traveling at a 143.13 degrees from the positive x axis towards the origin.

I am pretty lost as an approach on this problem, I am thinking I will have to use the equations that relate the exploded particles final positions to the position the center of mass would follow assuming no explosion. I have tried to do this but am only accounting for the helicopter alone and not the impact from the plane.

I am extremely confused and although my attempt is not very close to the answer I could at least use a hint in the right direction if possible.

2. Mar 19, 2012

### Staff: Mentor

Re: Dynamics: Systems of Particles. Airplane and Helicopter collision find final posi

Yes, first find the location of the center of mass on the ground as you suggest. The impact and fragmentation will not alter the motion of the center of mass thanks to conservation of momentum. What are the velocity components of the center of mass? How long does it "travel" after the collision?