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3 stars problem. Dimensional problem

Thai Pham


3.90 ... CP 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 850km/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 its rocket 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 degree above the horizontal.

For reasons of 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. You can ignore air resistance.

Your answer should include (i) a diagram showing the flight paths

of both the rocket and the airliner, labeled at several points with

vectors for their velocities and accelerations; (ii) an x-t graph

showing the motions of both the rocket and the airliner; and (iii) 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

I have no idea where to start?

Here is the diagram that draw, not sure if it is accurate

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I would start with the dimensions... if the rocket must cross the airplane's path 1km in front of airplane, and you also know the angle, you can use trig to determine how far the rocket should fall. Once you have this distance, it's just a free-fall problem! (I'm betting the diagram where you show the "must be at least 1 km away from airplane" is probably off. The line from the front of the airplane to the intersection of the plane's path and the rocket's path should be 1 km if I understand correctly.) Maybe try re-drawing the diagram, then seeing what you know from the triangle made up of the plane's path (horizontal line), the rocket's fall (vertical line), and the hypotenuse (the rocket's path).

Slick problem, I like it!

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