Calculate momentum

Question

Two 2.0Kg bodies, A and B collide. The velocities before the collision are ܸ஺

ሬሬሬ⃗ = 15݅ + 30݆ and

ܸ஻

ሬሬሬሬ⃗ = −10݅ + 5.0݆. After the collision, ܸ஺

ሬሬሬ⃗ = −5.0݆ + 20݆. All speeds are given in meters per

second. (a) What is the final velocity B? (b) How much Kinetic energy is gained or lost in the

collision? Ans: (a) 10i + 15j (b) 525 J

Answer 1

Hi Habeeb,

Something strange has happened to your query entry. It's not interpretable as is. Perhaps delete and reenter, using only regular text symbols. In particular the subscripts for the square boxes (if that is what they are), aren't informative, and the data given are strange (-5 + 20), (-10 + 5). Are these supposed to be x and y components of momentum? Your answer for (a) does suggest this. Please feel free to always check how queries you submit actually end up on Quora....

If so, first equate the momentum change for (A) as the opposite of the momentum change for (B). That will give a final velocity for B, and then rest is straightforward (conversion to net kinetic energies before and after). Remember that the momentum pieces may be treated individually per axis, whereas the kinetic energy sums the squares of the individual axis velocities (with the appropriate formulae!).