Question

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?

Answer 1

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)