In June 1997 the NEAR spacecraft, on its way to photograph the asteroid Eros, passed near the asteroid Mathilde. From photos transmitted by the spacecraft, Mathilde's size was known. It is presumably made of rock. Rocks on Earth have a density of about 3000 kg/m3 (3 grams/cm3). From the observations of the motion of the spacecraft as it passed Mathilde, scientists were able to learn something surprising about the asteroid.

In this problem you will analyze a similar situation. A spacecraft with mass 500 kg was traveling at nearly constant velocity with speed 12000 m/s. It flew past an asteroid, and the distance of closest approach (d in the diagram) was 3100 km (3.1e6 m). From photos taken by the spacecraft, it was determined that the asteroid had roughly the shape of a box 40 km by 30 km by 10 km (4e4 m by 3e4 m by 1e4 m).

Make a rough estimate of the vector change in momentum of the spacecraft that would result from encountering the asteroid. There is no one correct answer, since we're just trying to make a rough estimate. However, just because we're looking for a rough estimate doesn't mean that all answers are correct! Estimates that are wildly in disagreement with what physics would predict for this situation will be counted wrong.