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What is the speed of a garbage truck that is $1.20\times 10^{4}\textrm{ kg}$ and is initially moving at 25.0 m/s just after it hits and adheres to a trash can that is 80.0 kg and is initially at rest?
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Final Answer
$24.8 \textrm{ m/s}$
Solution Video

OpenStax College Physics Solution, Chapter 8, Problem 42 (Problems & Exercises) (1:25)

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Video Transcript

This is College Physics Answers with Shaun Dychko. A garbage truck is moving initially with a velocity of 25.0 meters per second and has a mass of 1.20 times 10 to the 4 kilograms and it then collides with an initially stationary trash can which has a mass of 80.0 kilograms and it sticks to the can and the question is what velocity will the truck and can have together after they are stuck together? The total initial momentum equals the the total final momentum and initially there's only momentum of the truck since the can is stationary initially and then after collision, the momentum is this combined mass of can plus truck multiplied by its velocity <i>v prime</i> that we have to find. And so we are gonna divide both sides by <i>m C</i> plus <i>m T</i> and then switch the sides around and we have <i>v prime</i> then is <i>m Tv T</i> over <i>m C</i> plus <i>m T</i>. So that's 1.20 times 10 to the 4 kilograms— mass of the truck— times its initial velocity of 25.0 meters per second divided by 80.0 kilograms plus 1.20 times 10 to the 4 kilograms here. And then you work that into your calculator and 24.8 meters per second will be the velocity after the can sticks to the truck.