Ashwat Prasanna
Dropping a projectile, and triangles
Imagine you stand at the tip of the Burj khalifa. Drop a coin. How long will it take to fall? Imagine a spaceship is going to self-destruct at 5km in the air, in 30 seconds. Will it hit you, on Earth, before it explodes?
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All of these (interesting) problems can be solved with the same equation. Let's look at a unique way it can be explained... without calculus.
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A fact is that for every second something drops, it speeds up by a fixed amount (9.8 m/s). So in two seconds, it will be travelling at around 20 m/s. This means that | speed = at | where a is acceleration. But, what is the sum of these (to find the distance)?
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Let's simplify by having | a = 10 | This means, after one second, it would have sped up to 10 m/s, and so would have also travelled 10m. The second second's speed would be 20m/s, and in the second second, the projectile would have travelled an additional 20m. Third second: 30m/s and an additional 30m. Seeing a pattern? But there is a small problem - what about fractional times? But there is a way to solve that...
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If we see this over time, we get a triangular shape:
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The shorter the time gaps, the more triangular
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And, the total distance is the sum of all the squares, which is the area of the triangle, which is | 1/2 base x height = 1/2 time x time = 1/2 time squared | units, which is that many times the acceleration.
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Finally, plugging this all in, we get the equation for the distance a projectile falls (from absolute stillness) = |d = 1/2 x g x t squared|
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This means that the spaceship will just narrowly miss Earth! Phew!
3Draw
Presenting… 3Draw! This is a tool that transforms your regular 2D drawing experience, and brings it to the 3rd dimension. You can pinch your fingers together to doodle, sketch or annotate what you see around you, with AR. And it’s 360°. It’s not just great for drawing. You can pull images off of screens into your workspace, and even enlarge them. Pinch your right thumb and index finger together to start drawing, just like how you would grasp a pen, and release when you’re done, or when you want to move it. Do the same on your left hand to take a screenshot of that region, move it around, and release when you’ve decided. Tap it again with your left hand to enlarge it. Lastly, you can add background images or colors (if you don’t want any background distractions), and you can customise the colors you use. When you’re done, just wipe your right hand, and erase the board
It uses an app that runs on your phone, put inside a VR headset, tracks your finger through VISION (which makes it iOS compatible), and draws along with it. It calculates the distance between your fingertips, and if it’s low enough, it starts to draw. It uses the phone’s gyroscope and accelerometer to track physical rotations, and re-orient the doodles and images. It takes a screenshot when you click with your left hand, and moves it around as well.