In order to calculate the velocity v of the combined mass after a collision, we must first consider each body’s momentum. Momentum is determined by multiplying an object’s mass by its velocity and is denoted as p=mv. In this instance, the initial momentum of each body can be found using the given information. The 4.2kg body has an initial momentum of mv = 42 kg⋅m/s and the 2.5kg body has an initial momentum of 25 kg⋅m/s due east (which is their direction before they collide).

When two objects collide perfectly inelastically, their total momentum remains constant but their velocities change since they combine into a single object with a different mass than either individual one did separately. This means that if we can find out what these new velocities are then we can easily calculate the value for v, which will be equal to both objects’ post-collision velocities since they have become one object moving together in that same direction at a single velocity.

To do so, we will use conservation of linear momentum which states that “if there is no external force acting on a system then total linear momentum is conserved; it does not change over time”. Therefore using our given data we can express this principle mathematically with: m1v1 + m2v2 = (m1+m2)v where v1 and v2 are our pre-collision velocities and m1 and m2 are our masses before collision respectively while v is our final post-collision velocity (since all masses combine into one thus having only one final velocity). We now need to solve for v so substituting in our data gives us: 42 kg⋅(10m/s) +25 kg⋅(0m/s) = (4.2 + 2.5)(V). Solving further yields V=7km/sec or 7000ms−1 as your answer!

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