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ID: 1882740 • Letter: E
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ecure www.saplinglearning.com/biscms/mod/jibis/view.php?id-6433143 Learning Jump to... 9/28/2018 10:00 PM 9.3/10 9/25/2018 01:41 PM Print CalcuatorPeriodic Table Question 18 of 20 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, eventu 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 ually emerging with a reduced, but still high, speed. As the after being hit was found to be moving with speed v, at angle 6, 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 w, 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 &, measured clockwise from the x-axis. 0.0250 kg M-45.0 kg 1550 m/s v,-0.315 mis 29.5 before after Number Number m/s e- Previous Check Answer Next ExtExplanation / Answer
from momentum conservation
total momentum remains same
along x axis
momentum before collsion = momentum after collsion
m*vo = (m*vb*costheta_b) + (M*vs*coshteta_s)
0.025*1550 = (0.025*vb*costheta_b) + (45*0.315*cos29.5)
vb*costheta_b = 1056.5
along y axis
momentum before collsion = momentum after collsion
m*0 = (m*vb*sintheta_b) + (M*vs*sinhteta_s)
0 = (0.025*vb*sintheta_b) - (45*0.315*sin29.5)
vb*sintheta_b = 279.2
vb = sqrt(1056.5^2+279.2^2) = 1092.8 m/s
theta_b = tan^-1(279.2/1056.5)= 14.8 degrees
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