Math can Launch One Bus with Speed minus Gravity

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The Mythbuster Angle to Launch a Bus Across the Gap

Launch Vertical versus Horizontal Distance : Image by Mike DeHaan

The Mythbusters built a ramp from a shipping container, which rose 110 inches, or 9.17 feet, over a 40-foot horizontal run. The angle of this ramp was 12.9 degrees.

The arctangent of (9.17/40 = 0.22925) = 12.9 degrees.

The total speed of the bus is 88 feet/second. Let’s calculate the vertical and horizontal components of the cannon ball’s launch from this ramp.

• The vertical velocity is 88*sin(12.9) = 19.65 feet/second.
• The horizontal velocity is 88*cos(12.9) = 85.8 feet/second.
• The cannon ball covers the 50 horizontal feet in 50/85.8 = 0.583 seconds.

The range equation for covering level ground is “Range = (speed^2)*sin(2 * launch angle)/gravity”.

• The cannon ball’s range is 88*88*sin(2*12.9)/32.15 = 104.8 feet.

So, the cannon ball would cover twice the horizontal distance of the gap, and reach a maximum height of six feet, if launched from the Mythbusters’ ramp.

Four Parting Notes for the Math to Launch One Bus

The first surprise is that, at about forty feet in length, a typical city bus almost spans the gap in the highway. However, at about 1:06 in the Mythbuster video, the fifty-foot gap in the diagram appears about twice the length of the bus. Here’s the video:

Secondly, in both the original Speed scene and the Mythbuster re-creation, the bus was somewhat damaged by the landing. The safest approach is to launch the bus upward from a ramp, then land at nearly the highest point of the parabolic trajectory. At the apex, the vertical speed is zero, so it will be a soft landing.

Third, the movie clip shows the bus launched at about 68mph and landed at 56mph.

View the launch at 0:17 in Colarusso’s clip here:

Let’s assume this was actual footage from the movie stunt jump. How did the bus lose 12mph?

• Climbing the ramp?
• Wind resistance during the jump?
• In the crash landing?

Our readers are free to determine the average deceleration assuming to air resistance, and recalculate the range.

The Jumpingbus clip shows the launch ramp (from 1:28) with the extra upward angle at the end, which accounts for the upward rotation of the nose of the bus (from 1:46). This was not a feature of the overpass shown in the movie. The damaging landing follows. From 2:22, it’s obvious that the tail of the bus starts falling immediately after leaving the ramp. Here’s the video – check it out yourself.

Finally, I question whether the bus truly launched at 60mph, since it did not appear to rise vertically or reach the horizontal distances from my calculations. Did it lose speed on the ramp, or was the stunt driver slower?

References for the Bus Launch in “Speed“

Launching a Cannon Ball : Image by benjcohen (Ben Cohen)

Colarusso, David. Could that actually happen? The bus jump from Speed. 2007. October 27, 2012. This video explanation includes physics and facts.

Discovery Networks. “MythBusters – Unarmed and Unharmed – Speed Bus Jump”. 2009. October 27, 2012. Can Grant Imahara launch a bus better than he can act?

Jumpingbus. “Speed 1994 (making of bus jump)”. 2009. October 27, 2012. This is a three-minute “making of” video with the best views of the stunt ramp.

Nave, R. “Trajectories“. Georgia State University. 2012. October 27, 2012. This page has excellent explanations and calculators.

raheelpervaiz. “Speed Bus Traverses Broken Highway Section”. 2009. October 27, 2012. This shows the movie jump, with the final speedometer at 56mph or so.

Richmond, Michael. “The ‘Speed’ bus jump“. Rochester Institute of Technology. Accessed October 27, 2012. This discusses the Mythbuster recreation, and has a link to a revealing “making of” video clip.

Author’s Note: We justify visiting a topic already covered by the Mythbusters since they covered one of ours. In June 2012, Decoded Science examined whether Jack and Rose could have survived, in “It Would Take a Titanic Raft of Flotsam to Float Two Actors“. That autumn, the Mythbusters devised a more elegant solution than my suggestion to nail several doors together. Canadian director James Cameron insisted, however, that the movie’s plot required Jack’s death.

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