A ball drops from the top of a tower. At the same time a rocket is launched from a different level of the tower. The height of the tennis ball in feet after (t) seconds can be represented by the quadratic function: b(t) = −t^2 − 2 + 36.

The height of Antonio's rocket after t seconds can be represented by the linear function: p(t) = −2t + 20.

(a) What are the two solutions to this system? Show your work.

(b) Explain which solution is not reasonable in this situation.

(c) After how many seconds do the rocket and the ball reach the same height