Skid numerical: moving vehicle hits parked vehicle

The moving vehicle (weight $W$) skids 40 m, hits the parked vehicle (weight $0.75W$) and both skid together 14 m. Work backwards: speed after impact, then momentum, then the 40 m skid.

Step 1: Speed after the collision (both vehicles together)

$$v' = \sqrt{2gfd'} = \sqrt{2(9.81)(0.62)(14)} = 13.050\ \text{m/s}$$

Step 2: Momentum conservation

The parked vehicle has zero speed before impact. With impact speed $u$ of the moving vehicle:

$$W\,u + 0.75W\,(0) = (W + 0.75W)\,v' \Rightarrow u = 1.75\,v' = 1.75(13.050) = 22.837\ \text{m/s}$$

Step 3: Initial speed before the 40 m skid

$$v_0 = \sqrt{u^2 + 2gfd} = \sqrt{(22.837)^2 + 2(9.81)(0.62)(40)} = 31.751\ \text{m/s}$$

Answer: initial speed of the moving vehicle = 31.75 m/s = 114.3 km/h (speed at impact 82.2 km/h).