A research rocket of mass is launched vertically from the deck of a ship at rest on…
PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
A research rocket of mass 75kg is launched vertically from the deck of a ship at rest on calm seas. For the first 3.0s after ignition, the rocket motor delivers a constant upward thrust of 1.20kN. Air resistance is negligible during this brief interval, and the mass of the rocket can be treated as constant.
Answer all parts thoroughly, showing symbolic work before substituting numerical values.
(a) Define an appropriate coordinate system and draw a clearly labeled free-body diagram for the rocket during the powered interval.
(b) Derive an expression for the rocket’s vertical acceleration in terms of the given symbols and fundamental constants.
(c) Calculate the numerical value of the rocket’s acceleration during the powered interval, including its sign.
(d) Determine the rocket’s velocity at the instant the motor shuts off (t=3.0s).
(e) Evaluate whether the rocket is still accelerating upward, downward, or not at all immediately after burnout, and justify your answer qualitatively without further computation.