A ball is dropped from a 200 foot cliff. If gravity is 32 ft/sec2, find the position function of the ball at time t. Using t^2 for t2.

Derek and Sandy leave an intersection at the same time. Derek travels north at 5 ft/s and Sandy travels west at 12 ft/s. Find a function that models the distance D between the pedestrians in terms of the time t (in seconds) elapsed since leaving the intersection.

A Ferris wheel has a radius of 30 m. Its center is 31 m above the ground. It rotates once every 40 s. Suppose you get on the bottom at t = 0. Write an equation that expresses your height as a function of elapsed time. Oh = 31 cos 2T- - O h = 30 cos 2T (t - 40) 40 = (t - 20) 40 Oh 31 cos 2T- = (t - 20) 40 (t – 20) 40 Oh 30 cos 2π- 2T +30 +1 +30 +31

A water tank is being drained and has the shape of a rectanuglar box 7m long, 6m wide and 5m high. How fast is the water depth changing when the water depth is 0.9m? V= 42(60-t)^2

The speed of a viral post is modeled by the function, Γ ( t ) = 3 squareoot 2t + 8e^t. If t is the number of hours passed since the initial posting, and Γ is the number of people (in thousands) per hour, how many people have seen the post from the initial post to hour eight?

An Astronaut on Mars drives a golf ball that moves according to the equations x=30t and y=74t−4.4t^2. (x and y in feet, t in seconds.)   Find the resultant velocity of the golf ball for t=2s.     Magnitude of the velocity of the ball =     Direction of the velocity of the ball =

During each cycle, the velocity (v in mm/s) of a piston is v=18t−18t^2, where t is the time in seconds. Find the displacement "s" of the piston after 0.25 seconds if the initial displacement is zero.   Round to 3 decimal places.  ____________mm

A light is placed on the tip of a windmill blade to protect planes from crashing into them. The windmill's center is 400 ft above the ground and the blades of the windmill are 180 feet long. The windmill rotates in the counter-clockwise direction and completes one full revolution every 10 seconds starting from the 3 o'clcok position. Define the function f that represents the light's distance above the ground in terms of the amount of time in seconds, t, since the windmill started rotating. Determine the equation of the midline for the function f. Graph the function using Desmos to check your answer. Assume y=f(t). Determine the amplitude of the function f. Graph the function using Desmos to check your answer.\ Determine the period of the function f. Graph the function using Desmos to check your answer.

A Ferris wheel has a diameter of 40 meters and rotates at a constant speed completing one full revolution every 2 minutes. If a person gets on the Ferris wheel at the bottommost point, express the person's height above the ground as a function of time, assuming the center of the Ferris wheel is at ground level.   Answer: The Ferris wheel has a diameter of 40 meters, which means the radius (r) is half of the diameter, i.e., (r = 20) meters. The Ferris wheel completes one full revolution every 2 minutes. The period (T) of the Ferris wheel is the time it takes to complete one full revolution. In this case, T = 2 minutes. The angular frequency (w) can be calculated using the formula (w = 2/?). Substituting the given value for (T): w = 2/? = ? radians per minute. Now, the height (h) of the person above the ground as a function of time (t) can be expressed using a sine function. The general form of a sine function is h(t) = A sin(wt+ϕ)+C where: - A is the amplitude (half the range of the…

Car A starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6 ft/s^2 until it reaches a speed of 60ft/s. Afterwards it maintains the speed. Also, when t = 0, car B located 6000 ft down the road is traveling towards A at a constant speed of 80 ft/s. Determine the distance traveled by Car A when they pass each other.Write the solution using pen and draw the graph if needed.