# Trolley A weighs 5kg and is moving at 15m/s to the right. It collides with a stationary Trolley B, weighing 10kg more than Trolley A. After the collision they move off together. Calulate the velocity that they move off with.

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To start with, we should work out all of the quantities we need:

Mass of Trolley A:  MA= 5kg

Mass of Trolley B: B weighs 10kg more than A

--> Therefore MB= 10 + 5 = 15kg

Mass of Both Trolleys together: MAB = 15 + 5 = 20kg

Initial Velocity of A: VA= 15 m/s

Initial Velocity of B: VB= 0 m/s

By the conservation of momentum, we know that the total momentum of a closed system is unchanged for any process. Thus the initial and final momenta of the two trollies combined are the same, ie:

PA + PB = PAB where P is momentum

We know that momentum P = mv

Therefore:

MAVA + MBVB = MABVAB

From above, we know all of these quantities except for VAB which is the quantity we need to find for the answer. Thus we can substitute in all of the values and find VAB:

(5x15) + (15x0) = (20xVAB)

75 = 20VAB

VAB = 75/20 = 3.75 m/s

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