1996 Paper 1 Q10

Year: 1996
Paper: 1
Question Number: 10

Course: UFM Mechanics
Section: Momentum and Collisions 1

Difficulty: 1500.0 Banger: 1516.0

momentum conservation of momentum kinetic energy explosion optimisation relative speed inequality

Problem

A spaceship of mass \(M\) is at rest. It separates into two parts in an explosion in which the total kinetic energy released is \(E\). Immediately after the explosion the two parts have masses \(m_{1}\) and \(m_{2}\) and speeds \(v_{1}\) and \(v_{2}\) respectively. Show that the minimum possible relative speed \(v_{1}+v_{2}\) of the two parts of the spaceship after the explosion is \((8E/M)^{1/2}.\)

No solution available for this problem.

Rating Information

Difficulty Rating: 1500.0

Difficulty Comparisons: 0

Banger Rating: 1516.0

Banger Comparisons: 1

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Problem source

A spaceship of mass $M$ is at rest. It separates into two parts in
an explosion in which the total kinetic energy released is $E$. Immediately
after the explosion the two parts have masses $m_{1}$ and $m_{2}$
and speeds $v_{1}$ and $v_{2}$ respectively. Show that the minimum
possible relative speed $v_{1}+v_{2}$ of the two parts of the spaceship
after the explosion is $(8E/M)^{1/2}.$

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