The 18000-kg F-35B uses thrust vectoring to allow it to take off vertically. In one maneuver, the pilot reaches the top of her static hover at 200 m. The combined thrust and lift force on the airplane applied at the end of the static hover can be expressed as F = (44t + 2500t2)i + (250t2 + t + 176580)j, where F and t are expressed in newtons and seconds, respectively.

Determine
(a) How long it will take the airplane to reach a cruising speed of 1000 km/hr (cruising speed is defined to be in the x-direction only),
(b) The altitude of the plane at this time.