A car drives horizontally off a cliff that is 30 meters high killing the driver on impact. The grieving widow claims her husband would never have driven faster than the posted speed limit of 35 mph and has hired a lawyer to sue the city for negligence. You are sent to investigate the crash site. You measure that the car landed 75 m from the base of the cliff [1 mph = 0.447 m/s]. A. Draw the detailed sketch for this motion with all of the relevant information, variables, and numbers contained in the sketch.
B. Write the three projectile equations with the known values and unknown variables placed into the equation.
C. Determine the time of fall. Then determine vix of the car as it flies off the cliff.
D. Based on what you were able to determine, assess whether the city is held liable for the accident

b) 0 = y₀ + 0 - ½ g t² ,  v₀ₓ = x / t

c)  v₀ₓ = 30.31 m / s

Explanation:

This is a projectile launching exercise, in your statement you have units of several systems, we are going to reduce everything to the SI system

   v = 35 mph (0.447 m / s / 1 mph) = 15.645 m / s

   y₀ = 75 m

A) In the attachment we can see a diagram of the movement of the vehicle in its fall

B) let's find the time for the fall to the base of the cliff (y = 0)

        y = y₀ + t - ½ g t²

when the vehicle leaves the cliff it goes horizontally, so its vertical speed is zero (v_{oy} = 0)

         0 = y₀ + 0 - ½ g t²

         t = √2y₀ / g

with this time we can use the equation of motion on the x axis

         x = v₀ₓ t

         v₀ₓ = x / t

C) we perform the calculations

            t = √ (2 30 / 9.8)

            t = 2.474 s

           v₀ₓ = 75 / 2.474

           v₀ₓ = 30.31 m / s

D) as we can see, the vehicle speed when leaving the cliff is almost twice the allowed speed (15.6 m / s)

therefore the city is not responsible for the accident