Unit 2 - Problem 2 => Man in elevator

The man weighs 800 newtons and wants to weigh 600 newtons. Find the man's mass first where gravity is 10 m/s/s. $$F = m*a$$ $$m = \frac{F}{a} = \frac{800}{10} = 80\;{kilograms} $$ Now find the acceleration that would make this mass weigh 600 newtons. $$a = \frac{F}{m} = \frac{600}{80} = 7.5\frac{m}{s^2}$$ The downward acceleration to reduce the overall acceleration is: $$ 7.5 = g - a_{down}$$ $$a_{down} = g - 7.5 = 10 - 7.5 = 2.5 \frac{m}{s^2}$$ The distance down traveled in 5 seconds, assuming starting from a dead stop, is given by: $$y_{down} = \frac{1}{2} a t^2 = .5 * 2.5 * (5*5) = 31.25 m$$