An object with mass m is launched with initial kinetic energy E0 at an angle θ = 45° with respect to the horizontal (+x). At the peak of its trajectory the object explodes, breaking into two pieces. The explosion adds an additional mechanical energy E0 to the system. After the explosion, one piece (mass m1) travels straight downward (-y) with an unknown speed v1 while the second piece (mass m2) travels with an unknown velocity →v2. The total mass m1+m2 = m is the same as before the explosion, but the mass ratio of the two pieces q = m1/m2 is unknown. Assume that the motion of the two pieces is in the xy-plane. (a) Find the velocity →v2 of the second piece and the speed v1 of the first piece in terms of E0, m, and q. (b) What is the maximum mass m1 (as a fraction of m) that is physically permitted given that it is traveling straight down after the explosion?
An object with mass m is launched with initial kinetic energy E0 at an angle θ = 45° with respect to the horizontal (+x). At the peak of its trajectory the object explodes, breaking into two pieces. The explosion adds an additional
(-y) with an unknown speed v1 while the second piece (mass m2) travels with an unknown velocity →v2. The total mass m1+m2 = m is the same as before the explosion, but the mass ratio of the two pieces q = m1/m2 is unknown. Assume that the motion
of the two pieces is in the xy-plane.
(a) Find the velocity →v2 of the second piece and the speed v1 of the first piece in terms of E0, m, and q.
(b) What is the maximum mass m1 (as a fraction of m) that is physically permitted given that it is traveling straight down after the explosion?
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