vertical motion formula

Question

A shovel drops down a mine shaft 5,000 feet deep. How much time will it take for the shovel to reach 3,400 feet above the bottom of the shaft?

Answer 1

height = 32*(-1/2)*t^2 +vt + s

v = 0 because we're dropping the shovel, not throwing it down

s = 0 from our starting point.

height = 5000 - 3400 = 1600 feet below the top of the shaft

-1600 = 32*(-1/2)*t^2

-1600 = -16*t^2

100 = t^2

t = 10

10 seconds.