A driver, accelerating too quickly on a horizontal bridge, skids, crashes through the bridge railing, and lands in the river 20.0 m below the level of the bridge roadway. (Continued in Description)

Question

The police find that the car is not vertically below the break in the railing, but is 53.6 m beyond it horizontally. Determine the speed of the car before the crash.

Answer 1

From the kinematic equation Δy = v_º t + 1/2 a t², -20 m = 0 - (9.8/2) t² because the car drops 20 m vertically with zero initial vertical velocity. From this, t² = 20/4.9 and t = 2.02 s. Horizontally, ignoring air resistance, this component of velocity is constant and we find it from Δx = v_x t: v_x = 53.6/2.02 = 26.5 m/s.