Q6. A rocket of mass m is projected vertically upwards with an initial velocity u from the ground. The rocket is subject to a resistive force of 4.905mv Newtons where v is the velocity of the rocket when it is x metres above the ground. (a) Derive a differential equation of the motion for the rocket, in the form: dv = -D(E +v) dx Where D and E are constants to be found. (b) Solve the differential equation and express x = f (v). (c) If u = 10 m/s find the greatest height the rocket reaches above ground.

Q6. A rocket of mass m is projected vertically upwards with an initial velocity u from the ground. The rocket is subject to a resistive force of 4.905mv Newtons where v is the velocity of the rocket when it is x metres above the ground. (a) Derive a differential equation of the motion for the rocket, in the form: dv = -D(E +v) dx Where D and E are constants to be found. (b) Solve the differential equation and express x = f (v). (c) If u = 10 m/s find the greatest height the rocket reaches above ground.