At a construction site a pipe wrench struck the ground with a speed of 31 m/s. (a) From what height was it inadvertently dropped? (b) How long was it falling?

Much easier if you work the questions in the reverse order.

b). Time = v/g

31m/s / 10m/s^2 = 3.1 seconds

a). Average speed during the fall = (1/2) (0+31m/s) = 15.5 m/s

Distance = (average speed) (time)

(15.5 m/s) (3.1 sec) = 48.05 meters

h = 48.05m

h = 48.05mt = 3.1 sec

Explanation:

v = 31 m/s

h = ?

Ek = Ep

0.5 mv² = mgh

h = v²/2g

h = 31² / (2*10)

h = 961/20

h = 48.05m

(b) h = 1/2 gt²

t = √2h/g

t = √ (2*48.05) / 10

t = 3.1 sec