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 mA = 17.2 kg and an initial velocity of nu Overscript bar EndScripts Subscript 0A = 8.50 m/s, due east. Object B, however, has a mass of mB = 28.3 kg and an initial velocity of nu Overscript bar EndScripts Subscript 0B = 4.65 m/s, due north. Find the (a) magnitude and (b) direction of the total momentum of the two-object system after the collision.

Explanation / Answer

momentum is conserved
momentum is a vector quantity (magnitude and direction)
so
M1 V1 + M2 V2 = (M1+M2) V3 (this is for an inelastic collision as in this problem)
taking N as 0° and E as 90°
[(17.2 * 8.5), 90°] + [(28.3 * 4.65) , 0°] = (M1 + M2) V3
these are at a right angle
so a^2 + b^2 = c^2 and tan(angle) with respect to north = E vector / N vector
giving

(146.2 , 90° ) + 131.6 ,0° = (M1 + M2) V3

sqrt(146.2^2 + 131.6^2) = 196.7

then direction is = 42 deg

(M1 + M2) V3 = 196.7, 42°

the magnitude and the direction of the total momentum is = 196.7 , 42 deg

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