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How about a physics problem?
A 170-pound paratrooper, on a raiding mission, is preparing to fling himself out of a C-130J gliding at 150 miles-per-hour at 500 feet above the ground. When you think about it, his gear usually totals in at about, say, 100 pounds, but the guy’s frightened, so he’s carrying a few extra clips for his standard-issue M16, a few extra grenades, and a few extra medical supplies, so we’ll round it out to 110 pounds.
This is the man’s first combat jump. His name is Jacob Reed.
In less than thirty seconds, Reed is going to barrel feet-first right out of his airplane, with 63 parachuting allies, and will go into freefall for three seconds. Then, he’s going to yank with all his might on his ripcord, and his parachute will flow gently out. If W right when he’s about to activate the parachute is 1,200 N, C is 0.4, ? is 0.7 lb/ft cubed, and A is 70 inches, solve for the drag, the time between jumping and touchdown, and the terminal velocity.
He is reminded of blood by the looming red lights. The lights are always this color during the night drops. His eyes dart around the bay, trying to hide his fear. Turribates, Brackenridge, Allen – they’re all on the verge of death, bleeding profusely, but they’re calm. Serene. Turribates would probably compare them to Hindu cows or something. Brackenridge smiles widely, clamps his hand on his back, and shouts an order to him. Brackenridge’s words are drowned out by the loud roars of the engine, but Reed nods regardless. Brackenridge cracks another huge smile, some would say it’s his defining feature, that wide, almost crazy grin. Out of the entire battalion, he’s the only one who likes these kinds of things.
The jump lights flash and begin to shine red. “Stand up!” calls the commander, and they do so.
“Check your equipment!” He traces the man ahead for any sign of a damaged wire or anything out of the ordinary. Nothing comes to his attention.
“Sound off!” The shouting of men comes down the bay, speeding towards him as he starts to make out what his allies are saying. “Twenty fine! Nineteen fine! Eighteen fine!”
Then, silence. He’s number seventeen, and he didn’t hear fine. He can feel himself about to throw up, his jaw shivering like it did when he was a boy, playing in the snow, his legs shaking. His mouth is a desert, he can’t feel any moisture in his body, his eyes are going weak and out of focus.
“Seventeen fine!”, the man next in line shouts. His vision slowly comes back to him, and he slaps the man just ahead of him. The rest of the men sound off. “One fine!”, the jumpmaster shouts. “Standby.” The ramp in the back lowers. Wind, rain, ice, fog, it all makes its way into the hangar, and as the engine backwash hits, the sound becomes borderline deafening. His legs start to shiver once again.
The light flashes green. The bile once again rises to his throat.
The first four of his comrades are already out of the airplane before he can grasp what’s happening. Now it’s his turn. He inhales as deeply as he can and quickly goes over the list within his head. His chin is glued to his throat, his elbows refuse to leave his sides, and his hands are spreading their fingers over his reserve parachute. He is hunched over, but he has no time to rest, he rushes towards the screaming wind of the open hatch.
His eyes are open.
And he jumps.
The howling air hits him hard, and he has to bend his back to keep from spinning out of control. He can feel the weather having it’s fun torturing him. The wind freezing his face in place, the fog blinding him completely, the rain shooting into his face like pellets at 150 miles per hour. He begins to count. One one-thousand. Two one-thousand. Three one-thousand. He hooks the ripcord and pulls. He feels the cable on his back whip through the channels on his parachute. The equipment which his life depends on launches. He braces himself for the coming jolt.
Jake Reed has 8 seconds before he crashes into the earth.
Everything stops. There is nothing but silence in his fall. He doesn’t feel the wind, nor the raindrops, nor the deafening roars of his airplane that he had just flung himself from. His mind begins to work at unnatural speeds, trying to figure out what has just happened with the parachute he’s trusting his life with. He yanks his knees to his chest, putting him into a fetal position. He looks up to find that his chute has become caught in its deployment container.
This makes things much more simple.
Now we can just use: time = distance/velocity.
He grabs for the cutoff strap on his shoulder as he tosses his ripcord. He rips away the strap and pulls on it with all of his might. His main chute detaches and gently floats away, while he goes into freefall.
He quickly slaps his hand over his reserve ripcord and yanks. The backup launches gracefully from its container and he goes from 150 miles per hour to below zero in less than a second. Just as he begins to loosen up, he is jerked to the right, and starts spiraling wildly. His reserve chute has collapsed.
He pulls and yanks and jerks on his guides as much as he can, refusing to allow himself to become what can only be described as a stain upon the earth, bodily material liquefied inside a pair of boots. He looks for his allies, but there is only fog. He doesn’t see the ground coming towards him at 176 feet per second.
And he never does.