A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The rocket's acceleration has components ax(t)=?t2 and ay(t)=???t, where ? = 2.50 m/s4, ? = 9.00 m/s2, and ? = 1.40 m/s3. At t=0 the rocket is at the origin and has velocity v? 0=v0xi^+v0yj^ with v0x = 1.00 m/s and v0y = 7.00 m/s.
1. Calculate the velocity vector as a function of time.
2. Calculate the position vector as a function of time.
Express your answer in terms of v0x, v0y, ?, ?, and ?. Write the vector v? (t) in the form v(t)x, v(t)y, where the x and y components are separated by a comma.
What is the maximum height reached by the rocket?
What is the horizontal displacement of the rocket when it returns to y=0?