Object A is moving due east, while object B is moving due north. They collide an

Question

Object A is moving due east, while object B is moving due north. They collide and stick together in a completely inelastic collision. Momentum is conserved. Object A has a mass of m_A = 17.0 kg and an initial velocity of V bar_0A = 7.46 m/s, due east. Object B, however, has a mass of m_B = 29.2 kg and an initial velocity of V bar_0B = 4.83 m/s, due north. Find the (a) magnitude and (b) direction of the total momentum of the two-object system after the collision. (a) = Number Units (b) theta Number Units north of east

Explanation / Answer

Momentum is conserved

PA + PB = P(A+B)

where PA is momentum of object A, PB is momentum of object B, P(A+B) is momentum of the two-object system after the collision

Break each vector down into its horizontal and vertical components

PA = (mAVA,0)

PB = (0,mBVB)

P(A+B) = (mAVA,mBVB)

The magnitude of the total momentum of the two-object system after the collision:

P(A+B) = sqrt[(mAVA + (mBVB)^2]

P(A+B) = sqrt[(17*7.46)^2 + (29.2*4.43)]

P(A+B) = sqrt[16083.3 + 16733]

P(A+B) = 181.15 kg/m^2

The direction of the total momentum of the two-object system after the collision:

theta = tan^-1(mBVB / mAVA) = tan^-1(16733/16083.3) = 46.11 degree north to the east

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