To determine the direction in which the suitcase accelerates, let’s analyze the forces at play here.

Given Data:

1. Mass of the suitcase, $m = 5.78 \, \text{kg}$
2. Force applied in the northern direction, $F_{\text{north}} = 30.4 \, \text{N}$
3. Force of friction in the eastward direction, $F_{\text{east}} = 8.92 \, \text{N}$

Approach:

Since the forces act perpendicular to each other (one to the north and the other to the east), we can determine the resultant force vector's direction using trigonometry. Specifically, we can use the tangent function to find the angle of acceleration relative to the north direction.

1. Calculate the Angle of Acceleration ($\theta$): $\theta = \tan^{-1}\left(\frac{F_{\text{east}}}{F_{\text{north}}}\right)$ Substituting the values: $\theta = \tan^{-1}\left(\frac{8.92}{30.4}\right)$

2. Calculate the Result: Solving this calculation: $\theta \approx \tan^{-1}(0.2934) \approx 16.4^\circ$

Conclusion:

The suitcase accelerates at an angle of approximately $16.4^\circ$ east of north. Since the angle is measured from the north towards the east, it’s a positive angle.

Answer:

$\text{Direction} = +16.4^\circ$

Would you like a deeper breakdown of any steps? Here are some related questions:

1. How do you calculate the magnitude of the resultant force in this scenario?
2. What effect does the frictional force have on the acceleration of the suitcase?
3. How would the angle change if the eastward frictional force were stronger?
4. How does the mass of the suitcase factor into calculating its acceleration?
5. What if there was a southward force; how would that affect the result?

Tip: For perpendicular forces, using trigonometric ratios like tangent is a quick way to find the direction of the resultant vector.