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(Solved): B. In a completely separate system, a rocket of mass \( m \) is projected vertically upwards from g ...
B. In a completely separate system, a rocket of mass \( m \) is projected vertically upwards from ground level with an initial speed of \( 40 \mathrm{~m} / \mathrm{s} \). The drag resistance has a magnitude of \( 3.27 \mathrm{mv} \). i. Draw a free body diagram of the system. ii. Derive the differential equation of motion of the rocket, and describe it in the form: \[ v \frac{d v}{d x}+\delta(v+\varepsilon)=0 \] Where \( \delta \) and \( \varepsilon \) are constants to be found. iii. Findan expression for the displacement of the rocket. Make sure your expression is in the form \( x=f(v) \). iv. Find the greatest height the rocket reaches above ground level.