In: Advanced Math
A 180-lb person jumps out of an airplane with initial upward velocity of 5 ft/s at a height of 3000 ft (assuming the air resistance is proportional to its falling speed). The air resists the body's motion with a force of 2 lb for each ft/s of speed. Assuming the constant gravity is 32 ft/s^2 (1) find its velocity v = v(t) (2) find its terminal velocity (3) find the distance of falling x = x(t) (4) find the duration in seconds until the body hits the ground