The forces are:
[tex]F_{grav} = 98,000 N[/tex], down
[tex]F_{net} = 80,000 N[/tex], down
[tex]F_{air}=18,000 N[/tex], up
Explanation:
We start by finding the force of gravity on the elephant, [tex]F_{grav}[/tex], which is given by
[tex]F_{grav}=mg[/tex] (downward)
where
m = 10,000 kg is the mass of the elephant
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
Substituting,
[tex]F_{grav}=(10,000)(9.8)=98,000 N[/tex]
Now we know that the net acceleration of the elephant is
[tex]a_{net}=8.0 m/s^2[/tex] downward
We can now use Newton's second law:
[tex]F_{net}=ma_{net}[/tex]
where [tex]F_{net}[/tex] is the net force on the elephant. Substituting, we find
[tex]F_{net}=(10,000)(8.0)=80,000 N[/tex]
and it also acts downward, since it has the same direction as the acceleration.
Finally, we can write the net force on the elephant as
[tex]F_{net}=F_{grav}-F_{air}[/tex]
where the force of gravity acts downward, while the air resistance ([tex]F_{air}[/tex] acts upward. The net force also acts downward, so it has the same sign of gravity.
Substituting:
[tex]F_{net}=80,000 N\\F_{grav}=98,000 N[/tex]
And solving, we find the air resistance:
[tex]F_{air}=F_{grav}-F_{net}=98,000-80,000 = 18,000 N[/tex] (upward)
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