A fireworks shell of total mass rises vertically and momentarily comes to rest at its…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Linear Momentum · Linear Momentum
Problem
A fireworks shell of total mass M rises vertically and momentarily comes to rest at its highest point, where it explodes into two fragments of masses m and M−m. The duration of the explosion is negligible compared with the time scale of the shell’s flight, and air resistance can be ignored.
(a) At the instant of the explosion, treat the two fragments together as a single system. Identify every external force acting on this system at that instant and argue whether the linear momentum of the system is conserved during the explosion.
(b) Immediately after the explosion, the smaller fragment moves horizontally due east with speed v0. Derive an expression for the speed of the larger fragment just after the explosion, and state its direction.
(c) 0.50s after the explosion, both fragments are still in flight. Ignoring air resistance, determine the horizontal separation between the fragments at that time.
(d) Consider the combined system of the two fragments plus Earth. Discuss whether the total linear momentum vector of this larger system changes from immediately before the explosion until long after both fragments have landed. Support your answer with physical reasoning.