A rocket is fired at an angle from the top of a tower of height ho = 50.0 m. Because of the design of the engines, its position coordinates are of the form x(t) = A + Bt2 and y(t) = C + Dt3 where A, B, C, and D are constants. Furthermore, the acceleration of the rocket 1.00 s after firing is if = (4.00i + 3.00]) m/s2. Take the origin of coordinates to be at the base of the tower. (a) Find the constants A, B, C, and D, including their SI units.
(b) At the instant after the rocket is fired, what are its acceleration vector and its velocity?
(c) What are the x- and y-components of the rocket's velocity 10.0 s after it is fired, and how fast is it moving?
(d) What is the position vector of the rocket 10.0 s after it is fired?