A model rocket with a mass of m = 0.100 kg is launched vertically. The engine’s thrust is T = 5.00 N, and this thrust is provided for 2.00 s. The squared velocity-to-force proportionality constant (due to air resistance), where the force of air resistance is in the direction opposite to that of the rocket’s travel, is ρ = 2.00x10^-4 kg/m. Thus, ρ*v² expresses the force on the rocket opposing its motion, where v is the rocket’s velocity.

Be careful to distinguish meters, m, from mass, m, in italics. Also, we’ll approximate that m remains constant for the duration of the rocket’s flight.

Write the differential equation for the powered portion of the rocket’s flight, with time the independent variable and velocity the dependent variable.

How fast, in m/s, is the rocket traveling at the instant the engine shuts off?

Write a second differential equation for the powered portion of the rocket’s flight, again with time the independent variable but with height above the launch pad the dependent variable.

How high, in m, is the rocket above its launch pad at this time?

Write the differential equation for the powered portion of the rocket’s flight, with time the independent variable and velocity the dependent variable.

How fast, in m/s, is the rocket travelling at the instant the engine shuts off?

Write a second differential equation for the powered portion of the rocket’s flight, again with time the independent variable but with height above the launch pad the dependent variable.

How high, in m, is the rocket above its launch pad at this time?