A test rocket is launched vertically upward from a well, a catapult gives its initial velocity $80$ m$/$s at the ground level $($y$=0$ m$).$ At that same instance its engines fire and accelerate upward at $3\mathrm{.}00$ m$/$s$2$ until it reaches an altitude of $1500$ m$.$ At the that ping its engines fail and the rocket goes in to $$free fall$$ with an acceleration $-9\mathrm{.}81$ m$/$s$2$

How long does the rocket stay above the ground?

What is the maximum altitude of the rocket?

What is the velocity if the rocket when it hits the ground:$$