Sapling Learning Far out in space, a bored astronaut fires an antique gun at a s

Question

Sapling Learning Far out in space, a bored astronaut fires an antique gun at a sack of rocks (mass M. The bullet (mass m) bounces around inside the sack a few times, eventually emerging with a reduced, but still high, speed. As the bullet flies off into space, the astronaut remembers with dismay that it was a priceless historical artifact. Fortunately, the astronaut knows the initial speed Vo of the bullet, and that the sack was initially at rest but after being hit was found to be moving with speed vs at angle 8s, as shown in the diagram. In what direction should the astronaut pursue the bullet, assuming that he starts from the initial location of the sack, and what minimum speed must he go faster than in order to catch up with it? Use the numerical values given below, and enter the direction as an angle 6 measured clockwise from the xaxis. m 0.0250 kg M-45.0 kg ve 1550 m/s v, 0.315 m/s 35.2 before after Number Number Go Previous Give up s view solution check Answer 0 Next Exit 8 Hint artner

Explanation / Answer

along vertical (y axis)

momentum before collison = momentum after collison

0 = M*vs*sinthetas - m*vb*sinthetab

M*vs*sinthetas = m*vb*sinthetab

45*0.315*sin35.2 = 0.025*vb*sinthetab

vb*sinthetab = 326.8 m/s

along horizontal

momentum before collison = momentum after collison

m*vo = (M*vs*costhetas) + (m*vb*costhetab)

0.025*1550 = (45*0.315*cos35.2) + (0.025*vb*costhetab)

vb*costhetab = 1087 m/s

vb = sqrt(1087^2+326.8^2) = 1135 m/s

tantheta b = (326.8/1087)

theta = 16.7 degrees

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