Problem. A model for the speed v(t) of a rocket at time t is given by the equation, v(t)=-gt-v, In m where 9 9.8 m/sec² (acceleration of gravity), m = 3 x 10' Kg (mass of the rocket plus fuel), r = at which the fuel decreases), and ve = 3 x 103m/sec (speed at which the exhaust gases are ejected). 160Kg/sec (rate the in of the speed v(t) in the neighborhood of t = 0; iv) Provide an analytical expression of the height h (t) with v (t) def dh/dt of the rocket at an arbitrary instant t after the liftoff; v) Which type of ordinary differential equation is satisfied by the hoight h(t)? Manifu