Please help with following applications of Sinusoids questions:

l. A carnival Ferris wheel with a radius of 14 m makes one complete revolution every 16 seconds. The bottom of the wheel is 1.5 m above the ground. If a person is at the top of the wheel when a stop watch is started, determine how high above the ground that person will he alter 1 minute and T seconds? Sketch one period of this mction. 2. The alternating half-daily cycles of the rise and fall of the ocean are called tides. Tides in one section of a bay caused the water to rise to 6.5 m above mean sea-level and to drop 6.5 m below. The tide completes one cycle every 12 hours. Find an equation that models the rise and fall of the tide and graph at least one period. 3. AFerris wheel has aradius of 12m andmakes one complete revolution every 12 seconds. Thehottom of the wheel is 2m above the ground. [F a person gets on at the bottom and goes up, determine how high the person will be after being on the ride for 5 minutes. 4. A water wheel has a radius of lllm 3m of the wheel is submerged under water. If the wheel makes one revolution and the bucket starts at the center and goes up, nd an equation that models the movement of the wheel's bucket and identify how high the bucket will be after it has moved 4!} degrees from its starting position. 5. John climbs on a roller coaster ad Six Flags. An observer starts a stopwatch and observes that John is at a maximum height of 12m at t = 13.2 a. At t = 14.5 s, John reaches a minimum height of4m. Assuming that the rollercoaster is sinusoidal, nd an equation that expresses John's height in terms of time. How high above the ground is John at t 211.8 s? 6. Johnny is driving his bike when a tack becomes stuck in his tire. The tire has a radius of 32 cm and makes one complete rotation every 500 milliseconds. How high will the tack be above the ground 12.38 seconds after becoming lodged in his tire? 7. Naturalists find that the population of foxes varies periodically with time. Records started being taken at t = 1} years. A minimum number, 200 foxes, occurred when t = 2.9 years. The next maximum, 800 foxes, occurred at t = 5.1 years. Give two different times at which the fox population is 625. 155 B. The average daily hours of sunlight, S, during a 12- 1, month period in a particular town is given by the mctiou 12 3(t) = a maa: rt} + d, where time, t, is measured in \"3 months, a and d are constants, and h is measured in degrees. The R graph of 5 versus t is shown. Find a complete equation including i values for a, h, and d which models the daily hours of sunlight in z the town, andgivethevaluesoftwhentheaveragedaily I 2 .1 i 5 , I, , mu\"! sunlightis lIIlI hours. 9. Two identical water waves pass a sensor in an oceanography laboratory. As the waves pass the sensor, the depth 1), in meters, of water is recorded and modelled by the function D(t) = 3.21 IDA-5 cos{24.2t) where t is the elapsedtime, in seconds, since the st wave bit the sensor. a. Find the minimum and maximum depths of the water as the two waves pass the sensor. b. Find the rst time after 16 seconds at which the depth of water reaches 3.5 m. III]. The mean depth, D, in meters of a mountain lake uctuates in a yearly cycle and can be modelled by the function i] (t) = acosct} + h, where t is the elapsed time, in months, since the beginning of an autumn season. The mean depth of the lake on month 1 is 33.2 m and on month 5 is 22.8 m. Find the mean depth of the lake on month 8