The following are problems I am stuck on for calculus. Please show all steps as well as including a detailed explanation of each. Thanks.

A 6 ft. tall person walks away from a 10-ft lamp post at a constant rate of 3 ft/sec. At what rate is the length of the person shadow increasing when the person is 10 ft from the pole?

A helicopter starting on the ground as rising directly into the air at a rate of 25 ft/sec. You are running on the ground starting directly under the helicopter at a rate of 10 ft/sec. Find the rate of change of the distance between the helicopter and yourself after 5 seconds.

A rocket is launch so that it rises vertically. A camera is positioned 5,000ft from the launchpad. When the rocket is 1,000ft above the launch pad its velocity is 600 ft/sec. Find the necessary rate of change of the camera's angle as a function of time so that it stays focused on the rocket.

Suppose you wish to approximate square root 8.98 using a linear approximating function L(x)=f(a) + f'(a)(x-a). Determine the function f(x) and the value of a that will accomplish this. Then determine the numerical error involved in the approximation.

An astronaut using a camera measures the radius of Earth as 4000 mi with an error of 80 mi. Use differentials to estimate the relative and percentage error of using this radius measurement to calculate the volume of Earth assuming the planet is a perfect sphere.