Answer the following word problems about applications of the derivative. Provide a complete solution. Thanks.

1. Rectilinear Motion. Valak jumps off a tower 1000 feet high with an initial velocity of 120 ft/sec. At the same time, Lorraine walks on the ground along the foot of the tower according to the equation of motion L(t) = t3 - 10t + 25t + 1, where L is Lorraine's directed distance at any time t from the point directly under the path of Valak's path of motion. What is Valak's equation of motion? ii. What is Valak's speed when he hits the ground? iii. At what time is Lorraine accelerating? iv. Upon hitting the ground, will Valak hit Lorraine? Explain. 2. Related Rates. The area of a circle is increasing at a rate of 2 in/s. If the initial radius of the circle is 1 in, find the rate of change of the radius of the circle when the radius is 15 inches. Compute the radius of the circle after 30x seconds? 3. Curve Tracing. Given the function f(x) = 3x5 - 20x3, graph the function analytically and identify the values of x where the function has the following: relative extrema ii. absolute extrema iii. points of inflection