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Will Nathan Drake make that leap in the Uncharted trailer?

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The time it takes for a drake to move in the vertical direction is the same as the time it takes for a drake to move horizontally. This means that I can use the horizontal movement to calculate the time, and then use the amount of time in the vertical movement to find its final vertical position.

When the drake makes a jump, he needs to climb to a vertical position of zero meters; This is the location of the slope and where I put the origin point. If this final value is less than zero meters, it descends below The Plane. This could be bad.

Determining horizontal movement is not difficult. Since it has a constant velocity, I can find its final horizontal position with the following equation:

Illustration: Rhett Allen

Check this out: I know the starting position x (x1 = 2.4 m) and final x position (x2 = 0 m) so I can use velocity x to find the time it takes to complete the jump. (It’s moving to the left, so it would be negative 3.37 m/s).

Note that in the trailer we don’t see the whole jump, but if we did, it would take 0.71 seconds to get to the back ramp of the plane.

Now, I can use this time and enter it into the vertical kinematic equation. This gives a final y-position of Negation 1.79 meters

This is less than zero, so there is nothing but air under it. And remember: this is bad.

We’re not done yet, but it’s worth wondering why it ended up minimum than it started. Because even though his initial velocity is in the positive direction (up), the jump takes so long that gravitational force stops his upward motion and makes him move downward at a faster and faster rate.

What about moving air?

When you stick your hand out the window of a moving car, you can feel something pushing you back. This is the interaction between your hand and the air molecules around the car – we call it air resistance. The amount of force you feel depends on the relative speed of the hand with respect to the air and the size and shape of your hand. At very large speeds, this air resistance force can be significant.

Let’s say the plane has a flight speed of 120 mph – I like this value because it’s the same as the terminal speed of a human parachute. When a person falls into the air for a period of time, the force of gravity causes their speed to increase. But this increase in velocity also increases the resistance of the air pushing upwards. Not long after the jump, the force of resistance of the upward air is equal to the force of downward gravity. This means that the total force is zero and the diver is no longer accelerating. Instead, they are now moving at a constant speed. We call that terminal velocity. Of course, humans can still adjust their bodies and interact with the air to get around and maneuver – which is why skydiving is still fun.


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