A cannonball of mass is fired from ground level with initial speed at an angle above…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A cannonball of mass m is fired from ground level with initial speed v0 at an angle θ0 above the horizontal. Neglect air resistance. At the highest point of its trajectory the cannonball explodes into two equal-mass fragments, A and B.
Immediately after the explosion, fragment A reverses its horizontal velocity component while its vertical velocity is still zero at that instant. Fragment B continues forward. The explosion itself is assumed to be instantaneous and internal to the two-fragment system.
(a) Derive an expression for the horizontal range Rintact that the cannonball would have traveled had it remained intact until it struck the ground.
(b) Determine the horizontal velocities of fragments A and B immediately after the explosion in terms of v0 and θ0. Show all steps in your reasoning.
(c) Calculate the horizontal landing positions xA and xB of fragments A and B, respectively, measured from the cannon. Express your answers in terms of v0, θ0, and g.
(d) Using your results, prove that the system’s center of mass lands at the same horizontal position as the intact cannonball would have landed.