In outer space rock 1, with mass 8 kg and velocity < 3200, -2900, 2600 > m/s, st

Question

In outer space rock 1, with mass 8 kg and velocity < 3200, -2900, 2600 > m/s, struck rock 2, which was at rest. After the collision, rock 1's velocity is < 3000, -2200, 2900 > m/s. What is the final momentum of rock 2?

Before the collision, what was the kinetic energy of rock 1?
K1i = ? J

After the collision, what is the kinetic energy of rock 1?
K1f = ? J

Suppose the collision was elastic (that is, no change in kinetic energy and therefore no change in thermal or other internal energy of the rocks). In that case, after the collision, what is the kinetic energy of rock 2?

K2f = ?J

K2f = ? J

Explanation / Answer

Using conservation of momentum

m1 V1i + m2 V2i = m1 V1f + m2 V2f

8 [3200 i - 2900 j + 2600] + 0 = 8 [3000 i - 2200 j + 2900k] + m2 V2f

final momentum of rock 2 = 8 [200 i - 700 j - 300 k] = 1600 i - 5600 j - 2400 k

for rock 1 :

V1f = 3200 i - 2900 j + 2600k = sqrt(32002 + (-2900)2 + 26002) = 5040.8 m/s

initial KE of rock 1 = (0.5) m V21i = (0.5) (8) (5040.8)2 = 1.02 x 108 J

for rock 1 :

V1f = [3000 i - 2200 j + 2900k] = sqrt(30002 + (- 2200)2 + 29002) = 4717 m/s

final KE of rock 1 = (0.5) m V21i = (0.5) (8) (4717)2 = 8.9 x 107 J

final KE of rock 2 = final KE of rock 1 = 8.9 x 107 J

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