The accompanying figure shows the velocity versus time curve for a rocket in out

Question

The accompanying figure shows the velocity versus time curve for a rocket in outer space where the only significant force on the rocket is from its engines. It can be shown that the mass M(t) (in slugs) of the rocket at time t seconds satisfies the equation M(t) =T/dv/dt where T is the thrust (in lb) of the rocket's engines and nu is the velocity (in ft/s) of the rocket. The thrust of the first stage of certain rocket is T = 7742019 lb. Use this value of T and the line segment in the figure to estimate the mass of the rocket at time t = 100. Round the final answer to the nearest thousand.

Explanation / Answer

at t =100,

dv/dt =(10000-5000)/(120-80)

dv/dt=125

given T=7742019

M(t)=T/(dv/dt)

M(100)=7742019/(125)

M(100)=61936.152

mass of rocket at time t =100 is=61936.152

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