(a) The total mass of the car and trailer is 1900 kg. The increase in kinetic energy (KE) is given by:

\(\frac{1}{2} \times 1900 \times 30^2 - \frac{1}{2} \times 1900 \times 20^2 = 475000 \text{ J}\)

The loss of potential energy (PE) is:

\(1900 \times g \times s \times \sin 5^{\circ}\)

Using the work-energy principle:

\(1900 \times g \times s \times \sin 5^{\circ} + 150000 = \frac{1}{2} \times 1900 \times 30^2 - \frac{1}{2} \times 1900 \times 20^2\)

Solving for \(s\):

\(s = 196 \text{ m}\)

(b) Using the equation \(v^2 = u^2 + 2as\):

\(30^2 = 20^2 + 2a \times 200\)

Solving for \(a\):

\(a = 1.25 \text{ m s}^{-2}\)

Applying Newton's second law to the trailer:

\(T - 100 + 500g \sin 5^{\circ} = 500a\)

Solving for \(T\):

\(T = 289 \text{ N}\)