Reference no: EM131015250
1. Solve the equation mx'' + βx' = mg for x(t), given that you step off the bridge-no jumping, no diving! Stepping off means x(0) = -100. x'(0) = 0. You may use mg = 160, β = 1, and g = 32.
2. Use the solution from Problem 1 to compute the length of time t1 that you freefall (the time it takes to go the natural length of the cord: 100 feet).
3. Compute the derivative of the solution you found in Problem 1 and evaluate it at the time you found in Problem 2. Call the result v1. You have found your downward speed when you pass the point where the cord starts to pull.
4. Solve the initial-value problem
mx'' + βx' + kx = mg, x(t1) = 0, x'(t1) = v1.
For now, you may use the value k= 14, but eventually you will need to replace that with the actual values for the cords you brought. The solution x(t) represents the position of your feet below the natural length of the cord after it starts to pull back.
5. Compute the derivative of the expression you found in Problem 4 and solve for the value of t where it is zero. This time is t2. Be careful that the time you compute is greater than t1-there are several times when your motion stops at the top and bottom of your bounces! After you find t2, substitute it back into the solution you found in Problem 4 to find your lowest position
6. You have brought a soft bungee cord with k = 8.5, a stiffer cord with k= 10.7, and a climbing rope for which k = 16.4. Which, if any, of these may you use safely under the conditions given?
7. You have a bungee cord for which you have not determined the spring constant. To do so, you suspend a weight of 10 lb. from the end of the 100-foot cord, causing the cord to stretch 1.2 feet. What is the k value for this cord? You may neglect the mass of the cord itself.
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