1 a. Caleb rides his bike with a constant speed of 8 miles per hour, How long will he take to travel a distance of 20 miles? S= D3D T=

A skydiver weighing 120kg drops vertically from a jet flying at 4.000m. Assume the force due to air resistance to be proportional to the velocity of the skydiver, with the proportionality constant b1= 20 N⋅sec/m before the cute is opened, and b2= 100 N⋅sec/m after the chute is opened. If the skydiver opens the chute after 60 seconds of free fall, find:  a. The total amount of time elapsed between dropping out of the plane and landing.  b. The velocity of the skydiver at the instant of landing on the ground.

The velocity v (in feet per second) of a rocket whose initial mass (including fuel) is m is given by as attached, where u is the expulsion speed of the fuel, r is the rate at which the fuel is consumed, and g = 32 feet per second per second is the acceleration due to gravity. Find the position equation for a rocket for which m = 50,000 pounds, u = 12,000 feet per second, and r = 400 pounds per second. What is the height of the rocket when t = 100 seconds?