In this scenario, we analyze a 1,000-kilogram rocket that is accelerating upwards due to thrust. The forces acting on the rocket include the weight force (force of gravity), thrust, and air resistance. The weight force, denoted as \( w \), is calculated as \( w = mg \), where \( g \) is the acceleration due to gravity, typically approximated as \( 10 \, \text{m/s}^2 \). Thus, for our rocket, \( w = 1,000 \, \text{kg} \times 10 \, \text{m/s}^2 = 10,000 \, \text{N} \).

The thrust force, \( F_t \), is given as \( 25,000 \, \text{N} \), while the air resistance, \( F_{\text{air}} \), is \( 5,000 \, \text{N} \). To find the net force acting on the rocket, we consider the upward direction as positive. Therefore, the net force \( F_{\text{net}} \) can be expressed as:

\( F_{\text{net}} = F_t - F_{\text{air}} - w \)

Substituting the known values, we have:

\( F_{\text{net}} = 25,000 \, \text{N} - 5,000 \, \text{N} - 10,000 \, \text{N} = 10,000 \, \text{N} \)

Using Newton's second law, \( F = ma \), we can solve for acceleration \( a \):

\( 10,000 \, \text{N} = 1,000 \, \text{kg} \times a \)

From this, we find:

\( a = \frac{10,000 \, \text{N}}{1,000 \, \text{kg}} = 10 \, \text{m/s}^2 \)

Now that we have the acceleration, we can use kinematic equations to find the final velocity after 20 seconds. The initial velocity \( v_0 \) is \( 0 \, \text{m/s} \), and the time \( t \) is \( 20 \, \text{s} \). We can use the equation:

\( v_f = v_0 + at \)

Substituting the known values:

\( v_f = 0 + (10 \, \text{m/s}^2)(20 \, \text{s}) = 200 \, \text{m/s} \)

Thus, the final velocity of the rocket after 20 seconds is \( 200 \, \text{m/s} \).