To capture requires two impulses. The first impulse changes the orbit so it has the required apogee and the second, some time later when the asteroid has arrived in the right place but wrong velocity, changes the velocity so apogee and perigee are correct. The asteroid will then be in orbit around earth where it may be picked over later at some convenient time.
Are we talking about detonations near the body or impulses from reaction motors attached to the surface?