Lesson 2 · from §78 of the 1910 text
The Falling-Body Curve
The falling-body curve
The curve below shows the distance a sphere of lead falls through the air in any number of seconds from 0 to 8. Time in seconds is measured along the bottom line (the x-axis, OX); distance in feet is measured up the side (the y-axis, OY).
The point A on the curve, just above 2, is opposite 64 on the distance scale: in 2 seconds the sphere falls 64 feet. Similarly B shows that it falls 256 feet in 4 seconds.
How far does a body fall in 6 seconds? The point on the curve above 6 is C. Opposite C on OY is 576. So in 6 seconds a body falls 576 feet.
How long does it take to fall 480 feet? Opposite 480 on OY is the point D on the curve. D is directly over a point midway between 5 and 6. So the body needs about 5\frac12 seconds.
(These values follow the rule d = 16t^2, which you can check: 16\cdot 6^2 = 576.)
Remember that no physical quantity can be measured perfectly and no graph can be drawn with perfect precision, so answers read from a graph are only approximately correct. They are, nevertheless, close enough to be extremely useful.
Try one:
Quick check
From the graph, how far does a body fall in 5 seconds?
Exercises
How to type math
Use ^ for powers (a^2), / for fractions ((a+b)/2), sqrt(x) for square roots, and cbrt(x) for cube roots. You can leave out the multiplication sign: 3ab means 3 \cdot a \cdot b. Mixed numbers like 4 1/2 work too. The preview under each box shows how your answer was read.
Use the falling-body graph above. Readings from a graph are approximate; answers within a few feet (or a tenth of a second) are accepted.
How far does a body fall in 8 seconds? 3 seconds? 7 seconds? 2\frac12 seconds? 6.2 seconds?
How many seconds does a body require to fall 400 feet? 196 feet? 100 feet? 25 feet? 120 feet? 750 feet?