A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The rocket's acceleration has components a(t)_x=alpha*t^2 and a(t)_y=beta-gamma*t, where alpha = 2.50 , beta= 9.00 , and gamma= 1.40 . At the rocket is at the origin and has velocity v_0=v_0xi+v_0yj with v_0x= 1.00 m/s and v_0y= 7.00 m/s. What is the maximum height reached by the rocket

Question

A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The rocket's acceleration has components a(t)_x=alpha*t^2 and a(t)_y=beta-gamma*t, where alpha = 2.50 ,  beta= 9.00 , and  gamma= 1.40 . At  the rocket is at the origin and has velocity v_0=v_0xi+v_0yj with  v_0x= 1.00 m/s and  v_0y= 7.00 m/s. What is the maximum height reached by the rocket