The same momentum closes an exact energy-momentum right triangle. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Momentum times speed limit is the motion leg
Momentum 15 kg m/s times speed limit 5 m/s gives motion-energy leg 75 J.
15⋅5=75
Energy and momentum close a right triangle
The total energy 125 J closes with motion leg 75 J and rest leg 100 J.