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Rockets are propelled by the ejection of the products of the combustion of fuel. Consider a rocket of total mass m, to be travelling at speed v, in a region of space where gravitational forces are negligible. Suppose that the combustion products are ejected at a constant speed v, relative to the rocket. Show that a fucl 'burn' which reduces the total mass of the rocket to mą results in an increase in the speed of the rocket to vz, such that Uz - V1 = v, In " m2 Suppose that 2.1 x 10° kg of fuel are consumed during a 'burn' lasting 1.5 x 10 s. Given that there is a constant force on the rocket of 3.4 x 10' N during this 'burn', calculate v,. Hence calculate the increase in speed resulting from the 'burn' if m, is 2.8 x 10° kg. What is the initial vertical acceleration that can be imparted to this rocket when it is launched from Earth, if the initial mass is 2.8 × 10° kg?

Rockets are propelled by the ejection of the products of the combustion of fuel. Consider a rocket of total mass m, to be travelling at speed v, in a region of space where gravitational forces are negligible. Suppose that the combustion products are ejected at a constant speed v, relative to the rocket. Show that a fucl 'burn' which reduces the total mass of the rocket to mą results in an increase in the speed of the rocket to vz, such that Uz - V1 = v, In " m2 Suppose that 2.1 x 10° kg of fuel are consumed during a 'burn' lasting 1.5 x 10 s. Given that there is a constant force on the rocket of 3.4 x 10' N during this 'burn', calculate v,. Hence calculate the increase in speed resulting from the 'burn' if m, is 2.8 x 10° kg. What is the initial vertical acceleration that can be imparted to this rocket when it is launched from Earth, if the initial mass is 2.8 × 10° kg?

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Rockets are propelled by the ejection of the products of the combustion of fuel. Consider a rocket of total mass m, to be travelling at speed v, in a region of space where gravitational forces are negligible. Suppose that the combustion products are ejected at a constant speed v, relative to the rocket. Show that a fuel 'burn' which reduces the total mass of the rocket to mą results in an increase in the speed of the rocket to vz, such that Uz - Uj = v, In "1. m2 Suppose that 2.1 x 10° kg of fuel are consumed during a 'burn' lasting 1.5 x 10 s. Given that there is a constant force on the rocket of 3.4 x 10' N during this 'burn', calculate v,. Hence calculate the incCrease in speed resulting from the 'burn' if m, is 2.8 x 10° kg. What is the initial vertical acceleration that can be imparted to this rocket when it is launched from Earth, if the initial mass is 2.8 × 10° kg?
Transcribed Image Text:Rockets are propelled by the ejection of the products of the combustion of fuel. Consider a rocket of total mass m, to be travelling at speed v, in a region of space where gravitational forces are negligible. Suppose that the combustion products are ejected at a constant speed v, relative to the rocket. Show that a fuel 'burn' which reduces the total mass of the rocket to mą results in an increase in the speed of the rocket to vz, such that Uz - Uj = v, In "1. m2 Suppose that 2.1 x 10° kg of fuel are consumed during a 'burn' lasting 1.5 x 10 s. Given that there is a constant force on the rocket of 3.4 x 10' N during this 'burn', calculate v,. Hence calculate the incCrease in speed resulting from the 'burn' if m, is 2.8 x 10° kg. What is the initial vertical acceleration that can be imparted to this rocket when it is launched from Earth, if the initial mass is 2.8 × 10° kg?
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