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Tie and Lift Math Problem

Take a long rope; tie it to the bottom of the goal post at one end of a football field.

Then run it across the length of the field (120 yards) to a goal post at the other end.

Stretch it tightly, and then tie it to the bottom of that goal post, so that it lies flat against the ground.

Now suppose that I add just 1 foot of slack to the rope, so that now I can lift it off the ground at the 50-yard line.

**How high can I lift it up?**

*(the answer is surprising)*
## 6 comments:

sqrt(60.5^2 - 60^2) = 7.7620873481300118644312308835865 yards. Except that i'm not that tall, so it'd be limited to a bit over 2 yards. Assuming a very, very non-stretchy rope. Perhaps we could make a space elevator with this stuff.

I think that is too much. The answer is closer to 13 feet. Got me thinking about when we round and how...

Stephen, are you mixing feet with yards?

Stephen, are you mixing feet with yards?

~12.26 ft so ~4 yds...

Opps. Feet. This is why we need the metric system. Crash and burn right into Mars.

sqrt((60 * 3 + .5)^2 - (g0 * 3)^2) = 13.4257215820975521971013596269 feet. Still higher than i can reach.

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