Question3. Two horizontal forces act on a $5.0-\mathrm{kg}$ mass. One force has a magnitude of 8.0 N and is directed due north. The second force toward the east has a magnitude of 6.0 N . What is the acceleration of the mass? A) $1.6 \mathrm{~m} / \mathrm{s}^{2}$ due north B) $1.2 \mathrm{~m} / \mathrm{s}^{2}$ due east C) $2.0 \mathrm{~m} / \mathrm{s}^{2}$ at 53 e N of E
ㅇ) $2.0 \mathrm{~m} / \mathrm{s}^{2}$ at $53 \mathrm{~m} E$ of N

Studdy Solution
Determine the direction of the acceleration.
The direction of the resultant force is given by the angle $\theta$ with respect to the east direction, which can be calculated using the tangent function:
$$\theta = \tan^{-1}\left(\frac{8.0 \, \text{N}}{6.0 \, \text{N}}\right)$$
$$\theta = \tan^{-1}\left(\frac{4}{3}\right)$$
$$\theta \approx 53^\circ$$
The direction is $53^\circ$ north of east.
The acceleration of the mass is:
$\boxed{2.0 \, \text{m/s}^2}$ at $53^\circ$ north of east.