4. The bridge over the Royal Gorge (a section on the Arkansas River in Colorado)

Question

4. The bridge over the Royal Gorge (a section on the Arkansas River in Colorado) is the highest bridge in America at 291 m above the river. Occasionally, thrill-seekers are allowed to bungee jump off the bridge. You are such a thrill-seeker, and attach yourself to a bungee cord and step off of the bridge. After leaving the bridge, you are in free fall for 25 m; at this point, the bungee cord starts to become taut and slows you down at a rate of 29.4 m/s 2 . (a) What is your velocity when the bungee cord starts to become taut? (b) How far above the water are you when the bungee cord stops you? (c) From the point where the cord starts to become taut, much time does it take the bungee to stop you? (d) At the point that the bungee starts to become taut, your car keys fall out of your pocket. How much time does it take them to reach the river? How fast are they going when they land?

Explanation / Answer

here,

height of the bridge , h = 291 m

(a)

free fall height , hf = 25 m

the velocity when the bungee cord start to became taut , v = sqrt( 2*g*hf)

v = sqrt( 2*9.8 * 25 )

v = 22.14 m/s

the velocity when the bungee cord start to became taut is 22.14 m/s

(b)

deaccelration due to cord, a = 29.4 m/s^2

let the height to stop be x

x = v^2 /2a

x = 22.14^2 / ( 2 * 29.4)

x = 8.33 m

height above the water = h - hf - x

the height above the water is 257.67 m

(c)

let the time taken be t

v = u + a*t

0 = 22.14 - 29.4 * t

t = 0.75 s

the time taken to stop is 0.75 s

(d)

let the time to reach the river be t'

and the final speed , v' = sqrt( 2*g*h)

v' = sqrt( 2*9.8 * 291)

v' = 75.52 m/s

the final speed when they reach water is 75.52 m/s

using first equationn of motion

75.52 = 0 + 9.8 * t'

t' = 7.71 s

the time to reach the river is 7.71 s

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