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

the diagram which shows forces as either balanced = same speed or unbalanced = accelerarting