Problems worthy of attack prove their worth by hitting back. —Piet Hein

Sunday, 8 March 2015

Tennis Ball Parabola

Here's an image of me throwing a tennis ball to Lottie:

Millie filmed the video and edited it down to a shorter segment. I turned the resulting video frames into a series of JPEGs by running:

ffmpeg -i Tennis\ Ball.mp4 tennis-%03d.jpeg

Then I composed them into a single image using ImageMagick:

convert -compose lighten tennis-014.jpeg tennis-015.jpeg \
-composite tennis-016.jpeg \
-composite tennis-017.jpeg \

-composite tennis-043.jpeg \
-composite result.jpeg

Millie then used Desmos (an online graphing editor) to superimpose a parabola on the image.

Update: Dima Spivak suggested I use the picture to estimate g, the acceleration due to gravity.
  • My head measures 0.22 m (chin to crown), and is 49 pixels on the picture.
  • The vertical distance, d, from the highest ball to the ball above Lottie's hands is 204 pixels, or 0.916 m.
  • The time, t, it took to travel this distance was between 12 and 13 frames (it's hard to say more precisely than this from the picture), which at 29.97 frames per second is between 0.4 and 0.434 seconds.
The acceleration is 2d/t2, which works out at between 9.7 and 11.4 m/s2. This range contains the accepted value of g, which is 9.8 m/s2.

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