91Ó°ÊÓ

The function $$ h(t)=-100 \cos \left(\frac{\pi t}{50}\right)+105 $$ represents the height \(h,\) in feet, of a seat on a Ferris wheel as a function of time \(t,\) where \(t\) is measured in seconds. (a) How high does a seat on the Ferris wheel go? (b) How close to the ground does a seat get? (c) If a ride lasts for 5 minutes, how many times will a passenger go around? (d) What is the linear speed of the Ferris wheel in miles per hour? Round to one decimal place.

Windshield Wiper The arm and blade of a windshield wiper have a total length of 34 inches. If the blade is 25 inches long and the wiper sweeps out an angle of \(120^{\circ},\) how much window area can the blade clean?

Show that the range of the tangent function is the set of all real numbers.

Motion on a Circle An object is traveling on a circle with a radius of 5 centimeters. If in 20 seconds a central angle of \(\frac{1}{3}\) radian is swept out, what is the angular speed of the object? What is its linear speed?

Show that the range of the cotangent function is the set of all real numbers.

Amusement Park Ride A gondola on an amusement park ride, similar to the Spin Cycle at Silverwood Theme Park, spins at a rate of 13 revolutions per minute. If the gondola is 25 feet from the ride's center, what is the linear speed of the gondola in miles per hour?

Lung Volume Normal resting lung volume \(V\), in mL, for adult men varies over the breathing cycle and can be approximated by the model $$ v(t)=250 \sin \left[\frac{2 \pi(t-1.25)}{5}\right]+2650 $$ where \(t\) is the number of seconds after breathing begins. Use the model to estimate the volume of air in a man's lungs after 2.5 seconds, 10 seconds, and 17 seconds.

A Blu-ray drive has a maximum speed of 10,000 revolutions per minute. If a Blu-ray disc has a diameter of \(12 \mathrm{~cm},\) what is the linear speed, in \(\mathrm{km} / \mathrm{h},\) of a point \(4 \mathrm{~cm}\) from the center if the disc is spinning at a rate of 8000 revolutions per minute?

The diameter of each wheel of a bicycle is 26 inches. If you are traveling at a speed of 35 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning?

The radius of each wheel of a car is 15 inches. If the wheels are turning at the rate of 3 revolutions per second, how fast is the car moving? Express your answer in inches per second and in miles per hour.