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enter image description here

The diagram represents speed-time for a sky diver. He falls freely from an aircraft then opens a parachute and later lands safely on the ground. At which point did the parachute fully open?

It's also not drawn quite right at the end. The speed definitely does not increase at any point after B.

My guess was B but it turned out to be C.

The answer presented:

The sky diver is falling under gravity known as free-falling at the beginning. The speed of the sky diver increases with time with decreasing acceleration till point B. The speed decreases when the parachute opens at point B. The parachute fully opens at point C.

Note: This questions ask (sic) which point did the parachute fully opened (sic), not when did the parachute just opened, (sic) which is point B.

Questions:

  1. In what way does a parachute not "fully" open?

  2. Is C necessarily THE point between B and D wherein the parachute fully opens? I was thinking C is merely the closest answer among A, B, C and D.

  3. Why does the diver speed up at a decreasing rate? Since the acceleration due to gravity is constant, I was thinking that the diver speeds up constantly.

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    $\begingroup$ 1. It does not instantly open, right, it takes time. 3. What do you know about terminal velocity? $\endgroup$
    – Bernhard
    May 17, 2015 at 12:26
  • $\begingroup$ @Bernhard What is your answer to #2? Terminal velocity is final velocity eg before object hits a wall or the ground $\endgroup$
    – Yami Yugi
    May 17, 2015 at 14:21
  • $\begingroup$ Terminal velocity is reached 5 to 10 seconds after jumping from a plane (long before you have a chance on hitting the ground). Terminal velocity is when the drag from air resistance equals the acceleration (due to gravity). The object remains at a constant velocity even though it is still falling. You described the final velocity (which might also be the same as the terminal velocity). $\endgroup$
    – LDC3
    May 17, 2015 at 15:15
  • $\begingroup$ I don't think the test maker had this mind but usually free fall parachutes have 2 canopies. Main canopy is large and will experience a huge force if opened at high speed that could rip it apart, damage the parachute and injure the parachutist (because of sudden great force). First they deploy a smaller canopy and when they've slowed down to near terminal velocity they deploy the main canopy to reduce the terminal velocity. $\endgroup$
    – Azad
    May 18, 2015 at 13:11
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    $\begingroup$ Apart from this, the graph also look suspicious. Parachute is fully open about the first point that you have greatest negative slope which should be a little after B. Immediately after B the slope should be somewhat gentler. And before D there's a small speed increase which is not real. The reason that the slope decreases between A and B is probably the drag of human body itself. $\endgroup$
    – Azad
    May 18, 2015 at 13:24

2 Answers 2

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  1. The parachute can not be opened instantaneously.

  2. The parachute is fully opened at the "vinicity" of the point $C$.

  3. The acceleration due to gravity is constant but there is another force one needs to take into account : the air resistance.

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Air drag is roughly proportional to the square of the velocity, the area of the object, the density of the air, and some "drag factor" that depends on the shape. For turbulent drag, we usually write

$$F = \frac12 \rho v^2 A C_D$$

In the case of the man falling from the plane, he will experience greater drag as his velocity goes up - so instead of linear acceleration, he will accelerate "more slowly" as his speed increases, until he reaches "terminal velocity" where the force of drag is equal to the force of gravity. For a human, this is around 200 km/h (depending on the position of the skydiver, etc).

Now as the parachute is opened, it will initially not have a large area, and not present the largest possible drag; but as it opens more fully (takes on its final shape), the force will increase and the deceleration will be greater. Then, as the man slows down, the drag from the parachute will decrease again.

With this in mind, you would expect the speed curve to have a corner when the parachute is first opened, but then become gradually steeper until the parachute is fully opened (but the speed is still high), then flatten again as the man slows down (with parachute fully deployed):

enter image description here

In this diagram you see that the parachute starts to open at B (corner) and is fully deployed at C (where the slope is steepest).

The graph does not really give you a clear situation of "deceleration getter bigger" like my graph does between B and C - but given that the slope of the given curve is greater at B than at C, I would answer "B". But I was never one for multiple choice...

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