A falling stone is at a certain instant 250 feet above the ground and 3 seconds later it is only 10 feet above the ground. From what height was it dropped?

Let h = the height (ft) from which the stone was dropped.

Assume that g = 32 ft/s² and ignore air resistance.

At time t seconds, the stone is 250 ft above ground. Therefore

(1/2) gt² = h - 250 (1)

After another 3 seconds, the stone is 10 ft above ground. Therefore

(1/2) g (t+3) ² = h - 10 (2)

Subtract (1) from (2).

(1/2) g[ (t+3) ² - t²] = 240

32 (t+3) ² = 480

(t+3) ² = 15

t = 0.873 s

From (1), obtain

16 * (0.873) ² = h - 250

12.194 = h - 250

h = 262.194 ft

Answer: 262.2 ft (nearest tenth)