The angle of elevation of the sun is decreasing at a rate of 0.25 rad/h. How fast is the shadow cast by a 400-ft-tall building increasing when the angle of elevation of the sun is $\pi/6$?

A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration of 22 ft$^2$. What is the distance traveled before the car comes to a stop?

The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation y=211.49-20.96 cosh 0.03291765x for the central curve of the arch, where x and y are measured in meters and |x| ≤ 91.20. Graph the central curve.

The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation

$$y=211.49-20.96 cosh0.03291765x$$

for the central curve of the arch, where x and y are measured in meters and |x| ≤ 91.20. What is the height of the arch at its center?

The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation

$$y=211.49-20.96 \cosh 0.03291765 x$$

for the central curve of the arch, where $x$ and $y$ are measured in meters and $|x| \leqslant 91.20$.

Graph the central curve.

The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation y=211.49-20.96 cosh 0.03291765x for the central curve of the arch, where x and y are measured in meters and |x| ≤ 91.20. At what points is the height 100 m?

A model for the velocity of a falling object after time t is

$$v(t)=\sqrt{\frac{m g}{k}} \tanh \left(t \sqrt{\frac{g k}{m}}\right)$$

where m is the mass of the object, g = 9.8 m/s$^{2}$ is the acceleration due to gravity, k is a constant, t is measured in seconds, and v in m/s. Calculate the terminal velocity of the object, that is,

$$\lim _{t \rightarrow \infty} v(t)$$

The gravitational force exerted by an object is given by F = mg , where F is the force in newtons, m is the mass in kilograms, and g is the acceleration due to gravity (9.81 m/s2).

Use the definition of the pascal to calculate the mass (in kg) of the atmosphere above 1 m2 of ocean.

A model for the velocity of a falling object after time t is

$$v(t)=\sqrt{\frac{m g}{k}} \tanh \left(t \sqrt{\frac{g k}{m}}\right)$$

where m is the mass of the object, g = 9.8 m/s$^{2}$ is the acceleration due to gravity, k is a constant, t is measured in seconds, and v in m/s. If a person skydives from a plane, the value of the constant k depends on his or her position. For a "belly-to-earth" position, k = 0.515 kg/s, but for a "feet-first" position, k = 0.067 kg/s. If a 60-kg person descends in belly-to-earth position, what is the terminal velocity? What about feet-first?

The weight (W) of an object is the product of its mass (m) in kilograms and g, the acceleration due to gravity in m/s2. If the acceleration due to gravity is 9.8 m/s2, find the corresponding weights for these masses, given in kilograms.

a) 22.1

b) 33.5

c) 41.3

d) 59.2

e) 78

The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation

$$y=211.49-20.96 \cosh 0.03291765 x$$

for the central curve of the arch, where $x$ and $y$ are measured in meters and $|x| \leqslant 91.20$.

What is the slope of the arch at the points in previous part?

A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 20 cpsh(x/20) - 15, where x and y are measured in meters. Find the slope of this curve where it meets the right pole.

How man y moles of lithium chloride are dissolved in 3.00 L of a 0.200 M solution of lithium chloride?

The wavelength of the yellow spectral emission line of sodium is 590 nm. At what kinetic energy would an electron have that wavelength as its de Broglie wavelength?