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)
