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.

155=7515\cdot5=75
Relativistic momentumMomentum is gamma times mass times speed.momentumspeedquiet leglimitbetagammamomentumclassical momentum

Energy and momentum close a right triangle

The total energy 125 J closes with motion leg 75 J and rest leg 100 J.

1252=752+1002125^2=75^2+100^2
Relativistic energyRest energy and motion energy form a triangle.speedquiet leglimitbetagammarest energymotion energytotal energy