Wednesday, April 09, 2008

The Physics of a Near Miss

Remember the story I posted about a SAAB driver who hit a bridge ramp at 85 mph? Not only did he survive, but he has since attempted to figure out the physics of what happened way back then. You can read the original story and the physics experiment here:

Ted's Wild Ride + Physics

I sent the link to Jim C., who made some corrections. According to him, Ted's math is off a bit. To be honest, I jumped off the train when sin, tan, and cosin began to fill our high school chalkboards. So, you'll have to consult a mathematician as you read the following explanation:
His math is off.

(85 miles/hr)*(1 hr/3600 sec)*(5280ft/mile) = 124.67 ft/sec

If the ramp is 30 deg, then the vertical velocity is v*sin(30) = 124.67ft/sec*sin(30) = 62.335 ft/sec

Assuming no air resistance:

1) Determine the time in the air

a = -32ft/sec^2
vv = a*t + vi
y = vi*t + 0.5*a*t^2

t = -2*vi/a = (-2)*(62.335ft/sec)/(-32ft/sec^2) = 3.896sec

3.896 sec is the time to go up and come back down


2) Determine the vertical distance

The time to reach the peak height is half the previous time (1.948 sec).

y = vi*t + *0.5*a*t^2 = (62.335ft/sec)*(1.948 sec) + (0.5)*(-32ft/sec^2)*(1.948 sec)^2 = 60.7 ft

60.7 ft is the max height.


3) Determine the horizontal distance

x = vh*t

vh = v*cos(30) = 124.67ft/sec*cos(30) = 107.97 ft/sec

x = 107.97ft/sec*3.896sec = 420.64ft


Of course, since the guy swerved before hitting the ramp and probably took his foot of the gas, he probably was going less than 85 mph at the top of the ramp. Not to mention the impact with the ramp itself.

See this link to mythbusters:
http://kwc.org/mythbusters/2006/09/special_megamovie_myths.html

They got a car to jump 172ft, but it wasn't drivable afterwards.

Still, an interesting story.
Jim

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