A scientist wishes to design a hand-held launcher that minimises the backward ‘kick’ felt by the user when a small probe of mass 0.25kg is projected forward.
(i) Derive an expression for the recoil velocity v of the launcher in terms of its mass M and the probe speed u (both measured with respect to the ground).
(ii) Using your expression, comment qualitatively on how increasing the mass of the launcher affects the user’s experience of the recoil.
(iii) The probe must leave at 60m/s. If the maximum recoil speed acceptable for comfort is 0.30m/s, find the minimum mass that the launcher should have.