To find the unbalanced force exerted by the arresting cables on the jet plane, we can use Newton's second law of motion, which states:
\[ F = m \cdot a \]
where:
- \( F \) is the force,
- \( m \) is the mass,
- \( a \) is the acceleration.
Given:
- The mass of the Hornet jet \( m = 1.3 \times 10^4 , \text{kg} \)
- The acceleration \( a = -27.6 , \text{m/s}^2 \) (the negative sign indicates deceleration).
Now we can substitute the values into the formula:
\[ F = (1.3 \times 10^4 , \text{kg}) \cdot (-27.6 , \text{m/s}^2) \]
Calculating this:
\[ F = 1.3 \times 10^4 \cdot -27.6 \]
\[ F = -35868 , \text{N} \]
The negative sign indicates that the force is acting in the opposite direction of the plane's motion (it is a decelerating force). The magnitude of the unbalanced force exerted by the arresting cables on the plane is:
\[ 35868 , \text{N} \]
Thus, the magnitude of the unbalanced force is 35868 N.