Chapter 5.3, Problem 29E

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

Calculus 441

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…