Rockets are propelled by the ejection of the products of the combustionof fuel. Consider a rocket of total mass m, to be travelling at speed v, ina region of space where gravitational forces are negligible. Suppose thatthe combustion products are ejected at a constant speed v, relative to therocket. Show that a fuel 'burn' which reduces the total mass of the rocketto mą results in an increase in the speed of the rocket to vz, such thatUz - Uj = v, In "1.m2Suppose that 2.1 x 10° kg of fuel are consumed during a 'burn' lasting1.5 x 10 s. Given that there is a constant force on the rocket of3.4 x 10' N during this 'burn', calculate v,. Hence calculate the incCreasein speed resulting from the 'burn' if m, is 2.8 x 10° kg.What is the initial vertical acceleration that can be imparted to thisrocket when it is launched from Earth, if the initial mass is 2.8 × 10° kg?

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