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.