I’ve run into a difficult math problem and I’m seeking advice from experts on how to solve it! ! !
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In the diagram, the plane takes off from point A and flies to point E at a speed of 500 meters per minute; passengers must parachute to point P, flying at a speed of 200 meters per minute. Question: From which point on line L in the diagram, that is, on the segment A–E, does it take the shortest time for a passenger to fly to point P?
200M/min – the speed is a bit slow; free fall from point D is the fastest option. It’s hard to say if the umbrella is open.
Is this speed of 200 the speed at which you’re moving from line AE towards point P? Without considering resistance, after parachuting, both the person and the airplane will maintain an AE-directional velocity of 500. The time it takes to cover the 200 meters at that speed, multiplied by 500, gives the shortest time required to start from point D. Whether jumping forward or backward, one needs to adjust position to reach point P
It is indeed a math problem; if it were a physics problem, point P would be an excellent starting point for making progress. Mathematically speaking, PD is not actually perpendicular; it can only be said to be approximately perpendicular. The reasoning is as follows: assume descent starts at point X, and the time taken is t. Then t = AX/500 + ((AD-AX)^2+PD^2)^0.5/200. Since AD = AB+BC+CD = 280+1030+460 = 1770, the equation becomes t = f(AX). By taking the derivative of this function and setting it to 0, the extreme value can be found; the corresponding value of t represents the shortest time required.
The coordinates of point P are not determined at all; what a stupid question. Parachuting involves a period of free fall, followed by the opening of the parachute which results in a quasi-decelerated motion, and then a constant velocity phase at 200 meters per minute; however, this figure is not accurate
Math problem: opening the parachute right at the moment of takeoff, or falling freely without a parachute. Ignoring all factors such as resistance, and considering only the conditions given in the question. Minutes are just a supplementary concept; you can replace them with years if you wish