Object A has mass mA = 8 kg and initial momentum vector pA, i = ( 22, -8, 0 ) kg · m/s, just before it strikes object B, which has mass mB = 12 kg. Just before the collision object B has initial momentum vector pB, i = (3, 5, 0) kg · m/s. The forces that A and B exert on each other are very large but last for a very short time. If we choose a time interval from just before to just after the collision, what is the approximate value of the impulse applied to the two-object system due to forces exerted on the system by objects outside the system?

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.