Question

Recall that the velocity of the free-falling bungee jumper can be computed analytically as [Eq. (1.9)]: v(t)= √(gm/c ) tanh (√gc/m t) where v(t) = velocity (m/s), t= time (s), 9 = 9.81 m/s2, m= mass (kg), Ca = drag coefficient (kg/m). (a) Use integral to compute how far the jumper travels during the first 8 seconds of free fall given m = 80 kg and ca = 0.2 kg/m. Hint: The answer is the integral over V(t) on the interval of [0,8]

Answer 1

To calculate the distance traveled by the bungee jumper in the first 8 seconds, we integrate the velocity function using the values g = 9.81 m/s^2, m = 80 kg, and c = 0.2 kg/m.

Step-by-step explanation:

To compute how far the bungee jumper travels during the first 8 seconds of free fall, we need to integrate the velocity equation v(t) = √(gm/c) × tanh(√gc/m × t) over the interval from 0 to 8 seconds. Given that g (acceleration due to gravity) is 9.81 m/s2, m (the mass of the jumper) is 80 kg, and c (the drag coefficient) is 0.2 kg/m, we'll perform the integration to find the distance traveled.

1. Setting up the integral, ∫ v(t) dt from 0 to 8.
2. Substituting the given values into the equation for v(t).
3. Using a mathematical software or table to find the integral.
4. Interpreting the result to find the total distance traveled in the first 8 seconds.