Problem 40P

(II) For an object falling freely from rest, show that the distance traveled during each successive second increases in the ratio of successive odd integers (1. 3. 5. etc.). (This was first shown by Galileo.) See Figs. 2-19 and 2-22.

FIGURE 2-19 MultiSash photograph of a falling apple, at equal time intervals. The apple falls farther during each successive interval, which means it b accelerating.

FIGURE 2-22 Example 2-10. (a) An object dropped from a tower falls wkh progressively greater speed and covers greater distance with each successive second. (Sec also Fig. 2-19.) (b) Graph of v vs. t.

Solution of 40P

The object in the figure is falling freely from rest. We will compare the displacements taken in each second.

y1 =? (the displacement taken in one second)

y2 =? (the displacement taken in 2 seconds)

y3 =? (the displacement taken in 3 seconds)

V0=0 (initial velocity)

g=9.8m/s2 (the sign is positive because we chose the downward positive)

Step 1 of 3