(a) Find free-body diagram in attachment (please rotate the picture, such that R points upward and mg points downward)
There are only two forces acting on the parachutist:
- Its weight, downward, of magnitude 1000 N, labelled with "mg" in the diagram (where m = mass of the parachutist, g = acceleration of gravity)
- The air resistance, upward, of magnitude 2000 N, labelled with "R" in the diagram
As the air resistance is larger than the weight, in the diagram it is represented with a longer arrow, in order to show the difference in magnitude.
(b) 1000 N, upward
By taking upward as positive direction, we can rewrite the two forces as:
R = +2000 N
mg = -1000 N
Where we have written the weight as a negative number, since its direction is downward.
Therefore, the net force on the parachutist will be
F = R + mg = +2000 + (-1000) = +1000 N
And the positive sign indicates that the resultant force is upward.
(c) The parachutist will be accelerated upward (= he/she will slow down)
We can answer this part by applying Newton's second law, which is summarized by the following:
[tex]F=ma[/tex] (1)
where
F is the resultant force on the body
m is its mass
a is its acceleration
For the parachutist in this problem, the mass is
[tex]m=\frac{mg}{g}=\frac{1000 N}{9.8 N/kg}=102 kg[/tex]
Therefore, using (1), we find the acceleration of the parachutist:
[tex]a=\frac{F}{m}=\frac{+1000}{102}=+9.8 m/s^2[/tex]
Where the positive sign indicates that the acceleration is upward. Therefore, the parachutist will be accelerated upward, which means that he/she will slow down, since its direction of motion was downward.
