A rocket fires vertically into the air with an upward thrust with a magnitude that is...

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A rocket fires vertically into the air with an upward thrust with a magnitude that is twice that of the force of gravity, during the first two seconds of flight. After the first two seconds the rocket engine is no longer providing any thrust. Let y(t) be the height of the rocket at time t,t 0. The initial height and velocity are zero. You may use the fact that the acceleration due to gravity is g 9.8 ms 2. Fix acceleration due to gravity to be in the negative y direction. = (a) (2 marks) Write down the differential equation for the motion of the rocket in the form (t) { for 0 2. (b) (3 marks) Solve this IVP to find the velocity y(t) and the position y(t) at time t 0. (c) (3 marks) Sketch (by hand) the graph of y(t) as a function of t. Label the intercepts clearly. (d) (3 marks) How high does the rocket reach? A rocket fires vertically into the air with an upward thrust with a magnitude that is twice that of the force of gravity, during the first two seconds of flight. After the first two seconds the rocket engine is no longer providing any thrust. Let y(t) be the height of the rocket at time t,t 0. The initial height and velocity are zero. You may use the fact that the acceleration due to gravity is g 9.8 ms 2. Fix acceleration due to gravity to be in the negative y direction. = (a) (2 marks) Write down the differential equation for the motion of the rocket in the form (t) { for 0 2. (b) (3 marks) Solve this IVP to find the velocity y(t) and the position y(t) at time t 0. (c) (3 marks) Sketch (by hand) the graph of y(t) as a function of t. Label the intercepts clearly. (d) (3 marks) How high does the rocket reach?