Recall that the velocity of the free-falling bungee jumper can be computed analytically as:

$$v(t)=\sqrt{\frac{g m}{c_{d}}} \tanh (\sqrt{\frac{g c_{d}}{m}} t)$$

where v(t) = velocity (m/s), t = time (s), g = 9.81 m/s$^{2}$, m = mass (kg), $c_{d}$ = drag coefficient (kg/m). (a) Use Romberg integration to compute how far the jumper travels during the first 8 seconds of free fall given m = 80kg and $c_{d}$ = 0.2kg/m.Compute the answer to $\varepsilon_{s}=1 \%$. (b) Perform the same computation with quad.

A bungee jumper falls 35 meters before his cord causes him to spring back up. He rebounds $\frac{2}{5}$ of the distance after each fall. What is the total vertical distance the jumper travels before coming to rest?

Use the formula to determine the value of the indicated variable for the values given. Use a calculator when one is needed. When necessary, use the π key on your calculator and round answers to the nearest hundredth.

$$A=\dfrac{1}{2}h(b_1+b_2)$$

; determine h when A=36,

$$b_1=4$$

, and

$$b_2=8$$

(geometry).

Find a value for w so that the equation has (a) two solutions and (b) three solutions. Explain your reasoning.

$$5 x ^ { 3 } + w x ^ { 2 } + 80 x = 0$$

Find the sum or difference.

$$\left( 5 x ^ { 2 } - 2 \right) + \left( 8 x ^ { 3 } + 2 x ^ { 2 } - x + 9 \right)$$

For the free-falling bungee jumper with linear drag, assume a first jumper is 70 kg and has a drag coefficient of 12 kg/s. If a second jumper has a drag coefficient of 15 kg/s and a mass of 80 kg, how long will it take her to reach the same velocity jumper 1 reached in 9 s?

$$w - 3 \frac { 2 } { 3 } = 1 \frac { 1 } { 2 }$$

Model the upward force on the bungee jumper as a linear relationship: F_U = −c'v, where c' = a first-order drag coefficient (kg/s). (a) Using calculus, obtain the closed-form solution for the case where the jumper is initially at rest (v = 0 at t = 0). (b) Use the Euler's method with stepsize 2s for a period of 12 s. The jumper leaps from a stationary hot air balloon. Mass of the jumper is 68.1 kg. Use a value of 11.5 kg/s for c'.

Write the vocabulary word that best completes the following sentence: Although the newspaper editor laughed at him, Wright somehow knew ___________ that the man was amused, not scornful.

The velocity of a falling parachutist is given by

$$\upsilon =\frac{gm}{c} (1 – e^{-(c/m)t})$$

where

$$g = 9.81 m/s^2.$$

For a parachutist with a drag coefficient c = 15 kg/s, compute the mass m so that the velocity is

$$\upsilon = 35 m/s$$

at t = 8 s. Use Excel, MATLAB or Mathcad to determine m.

The Centers for Disease Control and Prevention say that about 19.5% of teenagers smoke tobacco (down from a high of 38% in 1997). A college has 522 students in its freshman class. Is it likely that more than 25% of them are smokers? Explain.

The velocity

$$\upsilon$$

of a falling parachutist is given by

$$\upsilon = \frac{gm}{c} (1 – e^{-(c/m)t})$$

where

$$g = 9.81 m/s^2.$$

For a parachutist with a drag coefficient c = 15 kg/s, compute the mass m so that the velocity is

$$\upsilon = 36 m/s$$

at t = 10 s. Use the false-position method to determine m to a level of

$$\varepsilon_s$$

= 0.1%

Calculate the indefinite integral.

$$\int \left( 4 x ^ { 3 } - 2 x ^ { 2 } \right) d x$$

Without using any type of writing instrument, what can you do to make the following incorrect statement a correct statement? XI+I=X