A truck of mass 1750 kg is towing a car of mass 750 kg along a straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 7 - 2013 - Paper 2

Using the horizontal forces acting on the car, we have:

$T + 300 = 750(-1.02) \cdots (1)$

Where $T$ is the tension in the towbar. Solving for $T$:

$T = 750(-1.02) - 300$

Calculating gives:

$T = -765 \, \text{N}$

Thus, the force in the towbar is:

$T = 1553 \, \text{N}$

For the truck, considering the horizontal forces:

$T \cdot \cos(θ) - 500 - R = 1750(-1.02) \cdots (2)$

Replacing $T$ from equation (1):

$(1553 \cdot 0.9) - 500 - R = 1750(-1.02)$

Calculating:

$1397.7 - 500 - R = -1785$

Rearranging gives:

$R = 1397.7 - 500 + 1785$

Hence,

$R = 1750 \, \text{N}$