Question

How do I solve this?

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 mA = 16.6 kg and an initial velocity of nu Overscript bar EndScripts Subscript 0A = 8.92 m/s, due east. Object B, however, has a mass of mB = 29.2 kg and an initial velocity of nu Overscript bar EndScripts Subscript 0B = 4.44 m/s, due north. Find the (a) magnitude and (b) direction of the total momentum of the two-object system after the collision.

Answer 1

the vector sum of the initial momentums is equal to the final vector momenmtum

MaVaE+MbVbN=(Ma+Mb)V

well, let Ma' be Ma/(Ma+Mb)
and Mb' be Mb/(Ma+Mb)

V=Ma'*VaE+Mb'*VbN


magnitude..

V^2=(Ma'Va)^2+(Mb'*Vb)^2

direction (degrees N of E)

Theta=arctan((Mb'*Vb)/(Ma'*Va))

Answer 2

M1*V1 + M2*V2 = M1*V + M2*V
16.6*8.92 + 29.2*4.44i = 16.6V + 29.2V
148.1 + 129.6i = 45.8V
196.8[41.2o] = 45.8V
V = 4.3 m/s[41.2o]

a. Momentum = 196.8 kg-m/s

b. Direction = 41.2o N. of E.