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Don't Cliff Jump Like a Dummy-Use Physics

Don't Cliff Jump Like a Dummy-Use Physics
From Wired - February 15, 2018

I like to spend time outside when possible. On a recent adventure I took a couple of the kids to check out some trails near my mother's house. This particular place was pretty nice. It had a lake with some cliffs you could walk along. Note: Do not jump off the cliffs into the waterthere is a $500 fine for that (at least that's what the sign said).

As we were standing near the edge of one of these cliffs, my daughter said that it would not be too bad to jump offit's not that high. I was pretty sure it was higher than she thought it is. But I do not have to just guess; we can measure the height with just a rock, my phone, and physics.

Here's what you do. Take your phone and get ready to record some video. Now drop the rock from rest so that it falls into the water. If you have to toss the rock, that's fine, as long as you only throw it horizontally. Do not throw it up or downthis will give an inaccurate measurement for the height. The only thing you need from the video is the time it takes the rock to fall and hit the water. From this time, we can calculate the height.

For my cliff, I got a free fall time of 1.3 seconds (I got this using Tracker Video Analysisbut there are lots of other programs to get the time).

After you let go of the rock, there is essentially only one force acting on itthe gravitational force. This is a force that depends on the mass of the rock and the gravitational field (with a value on the surface of the Earth of 9.8 Newton/kilogram). We usually use the symbol g to represent this value. Since there is only one force on the rock, the rock will continue to speed up (accelerate)that's what constant forces do to an object.The acceleration of an object depends on both the force AND the mass.Since both the force and the acceleration depend on mass, in this case it cancels and you get an acceleration of g m/s2 in the vertical direction.That's why different mass rocks would hit the water at the same time (assuming the air resistance is negligible).

Now we know the acceleration of the falling rock.The acceleration describes the rate that the velocity changes. In this case, the starting velocity is zero m/s and the final velocity is unknown. This means that I can use the acceleration to find an expression for the final velocity (even though I do not really care about this). Oh, I am going to call the downward direction the positive direction just for fun and because coordinate systems are not real.

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