Question

a 48.7 kg passenger in a car is pushed forward with a force of 96.9 n by the car seat. the passenger is then shoved sideways by their sibling. if the passengers net acceleration is 2.44 \\(m/s^2\\), what is the force of the shove?

51.5 n
68.8 n
49.0 n
27.8 n

Explanation:

Identify given values and target unknown

We are given:

• Mass of the passenger, \(m = 48.7\text{ kg}\)
• Forward force from the car seat, \(F_{\text{forward}} = 96.9\text{ N}\)
• Sideways force from the sibling, \(F_{\text{sideways}}\) (target unknown)
• Net acceleration, \(a = 2.44\text{ m/s}^2\)

Calculate the net force

Using the Net Force Calculation knowledge point

$$ F_{\text{net}} = m \cdot a = 48.7\text{ kg} \times 2.44\text{ m/s}^2 = 118.828\text{ N} $$

Relate the perpendicular forces

Using the Pythagorean Theorem knowledge point

$$
LATEXBLOCK0
$$

Solve for the sideways force

Using the Pythagorean Theorem knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) 51.5 N
• (B) 68.8 N (Correct answer)
• (C) 49.0 N
• (D) 27.8 N