(Solved):
In a completely separate system, a rocket of mass \( m \) is projected vertically upwards ...
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. Find an 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.