Exercise 8.31: Asteroid Collision s of equal mass in the asterold belt Find the

Question

Exercise 8.31: Asteroid Collision s of equal mass in the asterold belt Find the speed of asteroid A after the collision. Two Mars and Jupiter collide with a glancing blow. Asterold A which was initially traveling at vA 40.0 m/s with respect to an inertial frame in which asteroid B was at rest, is deflected 30.0 from its original direction, while asteroid B travels at 45.0 to the original direction of A UA2 m/s Figure of 1 Part B Find the speed of asteroid B after the 40.0 m/s 30.0° m/s 45.0 Part C What fraction of the original kinetic energy of asteroid A

Explanation / Answer

from the conservation of momentum

m1u1+m2u2 = m1v1+m2v2

assume u1 = vA1

u2 = vB1 = 0

v1 = vA2

v2 = vB2

m1 = m2 = m

along the x axis

m1u1+0 = m1v1x+m2v2x

40 = v1cos30+v2cos45

40 = 0.866v1+0.707v2....(1)

along y axis

0+0 = m1v1sin30-m2v2sin45

v1sin30 = v2sin45

v2 = v1sin30/sin45 = 0.7072v1

substitute in equation 1

0.866v1+0.7072*0.707v1 = 40

v1 = 29.3 m/s = vA2

v2 = 0.7072*29.3 = 20.7 m/s = vB2

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