Dot Physics

How fast was the car going?

Reader Colin asked a great question about this popular clip.

How fast was the car moving?

First, a quick assumption. I will assume that the frame rate on the video is correct (meaning not slowed down). Colin already looked up the length of the Chevy Impala on Wikipedia for me. It has a length of 5.09 meters (I need that to scale the video).

This is the data I get from Tracker Video. The graph below is the x-position of the car with a line fit to the part of the motion before it hit the “ramp”. Note that since the car is moving to the left, it has a negative x-velocity.

i-b82af5889942cd12ce9a88ddaeaeac3e-2010-06-03_data_tool_4.jpg

So, this says the car is moving 24 m/s or 53 mph. Wow. Zooming fast for a toll booth. Notice the speed after the ramp.

i-6f0b006a33852891b259b50f92b06ad0-2010-06-03_data_tool_3.jpg

That is the same data with a line fit to the part of the motion after the ramp. This gives a x-velocity of 15 m/s or 33 mph. The car slows down because the ramp exerted a horizontal force on it in the direction opposite to the way it was moving. Now, how about the vertical motion?

i-03401e5bf89ffd772d0214380f18f82a-2010-06-03_data_tool_5.jpg

I don’t really have too many data points for while the car is in the air, but fitting a parabola to this data, I get a vertical acceleration of only 1.8 m/s2. That is odd. Let me try marking a different location on the car – this will give me a couple more frames of data. This is from the back end of the car.

i-6fa52590f25604d3612a0bd183ac4414-2010-06-03_data_tool_6.jpg

This gives a vertical acceleration of about 10 m/s2. That seems better. Here I had a good 4 frames of data using the back end. Notice that the vertical velocity before the ramp is positive. It looks like the back end of the car is coming up as though it were braking. Maybe.

Comments

  1. #1 Colin
    June 3, 2010

    Nice, thank you! :)

    The car does veer to the driver’s left while in the air so she must have hit it off CoG to the left, so perhaps that is skewing the 1.8 m/s^2?

  2. #2 tye
    June 3, 2010

    The car is definitely braking before the ramp as can be seen by the smoke coming from the tires.

  3. Hi Rhett,

    So many more questions. How high did the car go? How far did it go? How long was it airborne? If it landed on its wheels, with a reasonable assumption of the spring constants of the coil/leaf springs and seat springs, what was the maximum (de)acceleration of the passengers? The car is clearly rotating counterclockwise (when viewed from behind) along its longitudinal axis – given its airborne time, which face of the vehicle hit the ground?

    I wouldn’t expect answers immediately ;)

    Rob

  4. #4 Voodoo Idol
    June 4, 2010

    If the car was braking, as it has disc brakes in the front at the bare minimum, the front end would likely have dipped instead of lifting up.

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