Will Nathan Drake make that leap into the Uncharted trailer?

The time it takes Drake to move vertically is exactly the time it takes him to move horizontally. This means that I can use horizontal motion to calculate time and then use that amount of time in vertical motion to find its final vertical position.

When Drake makes his jump, he must rise to a vertical position of zero meters; this is the position of the ramp and the place where I set the start. If this end value is less than zero meters, it lands Below The plane. And that would be bad.

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

Illustration: Rhett Allen

Look at this: I know the starting position on x (x1 = 2.4 m) and the final x-position (x2 = 0 m) so that I can use the x-speed to decide the time required to complete the jump. (It moves to the left, so it will be minus 3.37 m / s.)

Note that we don’t see the whole jump in the trailer, 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 include it in the vertical kinematic equation. This gives the final y-position of negative 1.79 meters.

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

We’re not ready yet, but it’s worth taking a second to wonder why it’s even short than he started. This is because although its initial velocity is in a positive (upward) direction, the jump takes so long that gravitational force stops its upward movement and causes it to move downward at a faster and faster speed.

How about moving air?

When you run your hand through the window of a moving car, you may feel something push you back. This is the interaction between your hand and the air molecules around the car – we call this air resistance. The amount of force you feel depends on the relative speed of your hand relative to the air and the size and shape of your hand. At very high speeds, this force of air resistance can be significant.

Let’s say that the plane has a flight speed of 120 mph – I like this value because it is the same as the final speed of a paratrooper. When someone falls in the air for a while, the gravitational force makes them increase their speed. But this increase in speed also increases the air resistance upwards. At some point not long after the jump, the force of the air resistance is equal to the gravitational force down. This means that the total force is zero and the diver no longer accelerates. Instead, they are now moving at a constant speed. We call this top speed. Of course, people can still adjust their bodies and interact with the air to rotate and maneuver – which is why skydiving is still fun.

Source link