A 4.5 kg aerial shell explodes at the top of its flight into three fragments that…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Linear Momentum · Linear Momentum
Problem
A 4.5 kg aerial shell explodes at the top of its flight into three fragments that separate in the same horizontal plane. Fragment 1 has mass 2.0 kg and moves at 25 m s⁻¹ due north. Fragment 2 has mass 1.0 kg and moves at 30 m s⁻¹ due east. Fragment 3 has mass 1.5 kg. Air resistance during the very short explosion interval is negligible.
(a) Construct a labeled vector diagram that places the momentum vectors of fragments 1 and 2 head-to-tail in the order they were listed.
(b) On the same diagram, complete the vector polygon so that the polygon closes, thereby representing conservation of momentum for the isolated system. The closing side represents the momentum of fragment 3. Measure or otherwise determine the magnitude and direction of this momentum.
(c) Using your result from part (b), calculate the speed of fragment 3.
(d) Provide a written justification, referencing both the diagram and physical principles, for why the direction you found for fragment 3 must be unique if total external impulse is negligible.