A rocket designed to place small payloads into orbit is carried to an altitude of 12.0 km above sea level by a converted airliner. When the airliner is flying in a straight line at a constant speed of 850 km/h, the rocket is dropped. After the drop, the airliner maintains the same altitude and speed and continues to fly in a straight line. The rocket falls for a brief time, after which its rocket motor turns on. Once that motor is on, the combined effects of thrust and gravity give the rocket a constant acceleration of magnitude 3.00g directed at an angle of 30.0° above the horizontal. For safety, the rocket should be at least 1.00 km in front of the airliner when it climbs through the airliner's altitude. Your job is to determine the minimum time that the rocket must fall before its engine starts. Ignore air resistance. Your answer should include (a) a diagram showing the flight paths of both the rocket and the airliner, labeled at several points with vectors for their velocities and accelerations; (b) an x – t graph showing the motions of both the rocket and the airliner; and (c) a y – t graph showing the motions of both the rocket and the airliner. In the diagram and the graphs, indicate when the rocket is dropped, when the rocket motor turns on, and when the rocket climbs through the altitude of the airliner.
A rocket designed to place small payloads into orbit is carried to an altitude of 12.0 km above sea level by a converted airliner. When the airliner is flying in a straight line at a constant speed of 850 km/h, the rocket is dropped. After the drop, the airliner maintains the same altitude and speed and continues to fly in a straight line. The rocket falls for a brief time, after which its rocket motor turns on. Once that motor is on, the combined effects of thrust and gravity give the rocket a constant acceleration of magnitude 3.00g directed at an angle of 30.0° above the horizontal. For safety, the rocket should be at least 1.00 km in front of the airliner when it climbs through the airliner's altitude. Your job is to determine the minimum time that the rocket must fall before its engine starts. Ignore air resistance. Your answer should include (a) a diagram showing the flight paths of both the rocket and the airliner, labeled at several points with vectors for their velocities and accelerations; (b) an x – t graph showing the motions of both the rocket and the airliner; and (c) a y – t graph showing the motions of both the rocket and the airliner. In the diagram and the graphs, indicate when the rocket is dropped, when the rocket motor turns on, and when the rocket climbs through the altitude of the airliner.
Related questions
Question
Transcribed Image Text:A rocket designed to place small payloads into orbit is carried to an altitude
of 12.0 km above sea level by a converted airliner. When the airliner is flying in a straight
line at a constant speed of 850 km/h, the rocket is dropped. After the drop, the airliner
maintains the same altitude and speed and continues to fly in a straight line. The rocket
falls for a brief time, after which its rocket motor turns on. Once that motor is on, the
combined effects of thrust and gravity give the rocket a constant acceleration of magnitude
3.00g directed at an angle of 30.0° above the horizontal. For safety, the rocket should be at
least 1.00 km in front of the airliner when it climbs through the airliner's altitude. Your job
is to determine the minimum time that the rocket must fall before its engine starts. Ignore
air resistance. Your answer should include
(a) a diagram showing the flight paths of both the rocket and the airliner, labeled at several
points with vectors for their velocities and accelerations;
(b) an x
t graph showing the motions of both the rocket and the airliner; and
t graph showing the motions of both the rocket and the airliner. In the diagram
(с) а у
and the graphs, indicate when the rocket is dropped, when the rocket motor turns on,
and when the rocket climbs through the altitude of the airliner.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps with 9 images
