00:01
So in this question, we have a rocket that was originally traveling at 6 ,600 meter per second.
00:13
And then in an explosion, it's separated into two fragments.
00:18
And each section, let's just assume they're traveling in the same way, and they have a relative velocity of 2 ,800 meter per second.
00:29
And they have equal masses.
00:32
So that if the original mass is m, they would both be half of m.
00:38
Let us first try to write down the conservation of momentum.
00:42
So this causes v and these causes a, causes b.
00:50
So we have va and vb.
00:54
So before the explosion, we have mv.
00:59
After the explosion, we have ma, which is just half of m times va.
01:05
Plus mb which is also half of m times bb so we can cancel m here and this gives us v equals 1 half v a plus bb and since this is this is v relative this is v we already know what v is but we are trying to find both v and vv and to do that we first need to cancel one term let's say let's use this relative velocity to cancel bb so bv equals to v a minus v relative if we plug that into this equation we have v equals half of two v a minus v relative and from that we can find va va equals v plus half of v relative so that is 60 100 meters per second plus 1 half, so that is 14 meters per second.
02:20
And that is 8 ,000 meters per second.
02:25
And what about vb? vb equals va minus v relative equals 8 ,000 meter per second minus 2800 meters per second, which is equal to 52 hundred meters per second.
02:44
So that is the velocity of section a and section b...