Question

When does a skydiver achieve terminal velocity? when gravity equals air resistance when gravity is greater than air resistance when air resistance acts on the diver and gravity does not when gravity acts on the diver and air resistance does not

Answer 1

Answer:

when gravity equals air resistance

Explanation:

There are two forces acting on a skydiver falling down:

1) Gravity - this force acts downward, and it is constant during the whole fall, because its magnitude is given by

$F=mg$

where m is the mass of the skydiver and g the gravitational acceleration. Both quantities are constant, so the force of gravity is constant.

2) Air resistance - this force acts upward, and it is not constant: it is proportional to the velocity of the skydiver

$F=kv$

where k is a constant and v is the velocity. Therefore, as the skydiver falls down, its velocity increases and the air resistance increases as well.

The equation of forces for the skydiver is therefore:

$mg-kv=ma$

where a is the skydiver's acceleration. At the beginning of the fall, $mg>kv$, so the skydiver accelerates towards the ground. However, as he accelerates, the air resistance $kv$ increases, till the moment at which air resistance becomes equal to gravity:

$mg=kv$

when this condition occurs, then the acceleration becomes zero, so the skydiver no longer accelerates and continues his fall at constant speed. This constant speed is called terminal velocity, and so it occurs when

gravity equals air resistance

Answer 2

When gravity Equals air resistances