An energy-efficient hard drive has a 2.7-in diameter and spins at 4400rpm A point on the edge spins at approximately  in/min .       .

It takes jupiter 11.64 yr to complete one circular orbit around the sun. If jupiter's avarage distance from he sun is 483,600,000 miles, what is it's linear speed in miles/sec?

A lighthouse is located on a small island 4km away from the nearest pointP on a straight shoreline, and its light makes 6 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 2km from the point P?

A security camera is centered 50 feet above a 100-foot hallway. It is easiest to design the camera with a constant angular rate of rotation, but this results in recording the images of the surveillance area at a variable rate. So, it is desirable to design a system with a variable rate of rotation and a constant rate of movement of the scanning beam along the hallway. Find a model for the variable rate of rotation when ∣dx/dt∣ = 2 feet per second.

A rocket will carry a communications satellite into low Earth orbit. Suppose that the thrust during the first  200   sec  of flight is provided by solid rocket boosters at different points during liftoff. The graph shows the acceleration in G–forces (that is, acceleration in  9.8 – /msec2  increments) versus time after launch.

A car drives on a circular track with a radius of 1 km. At the southernmost point of the course is a radar meter. At a given time, the car is 1/2 km from the meter and the distance between the car and the meter increases by 50 km/h. How fast is the car driving north?

A lighthouse is located on a small island 3km away from the nearest point P on a straight shoreline and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1km from P?

A rectangular beam is to be cut from a cylindrical log of diameter 20cm. Express the cross sectional area of the beam as a function of the angle.

A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline. Its light makes 5 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 0.7 kilometers from P?

A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 30 ft from the pole? 16/3 X ft/s Enhanced Feedback Please try again. Draw a diagram for this problem. Draw a right triangle with horizontal and vertical edges. Let the vertical edge be the pole. Draw another vertical line with one end on the hypotenuse: and the other end on the horizontal edge depicting the man. Label the distance between the man and the pole x and the distance between the man and the tip of the shadow y. Use properties of similar triangles to find a relation among x, y, the height of the man, and the height of the pole. Differentiate this equation with respect to time, t, using the Chain Rule, to find the equation for the rate at which the tip of the shadow is moving, (x + y). Then, use the values from the exercise to evaluate the rate of change of the distance between the…