Questions: Find acceleration Horizontal and Vertical

Solution Steps

• The forces acting on the object are:
  • 15 N to the left (negative x-direction)
  • 9 N upward (positive y-direction)
  • 7 N downward (negative y-direction)
  • 5 N at an angle of 30° below the horizontal (both x and y components)

• The 5 N force at 30° can be resolved into horizontal (x) and vertical (y) components:
  • \( F_{5x} = 5 \cos(30°) = 5 \times \frac{\sqrt{3}}{2} = 4.33 \, \text{N} \) (positive x-direction)
  • \( F_{5y} = 5 \sin(30°) = 5 \times \frac{1}{2} = 2.5 \, \text{N} \) (negative y-direction)

• Sum of forces in the x-direction:
  • \( F_{x} = -15 \, \text{N} + 4.33 \, \text{N} = -10.67 \, \text{N} \)
• Sum of forces in the y-direction:
  • \( F_{y} = 9 \, \text{N} - 7 \, \text{N} - 2.5 \, \text{N} = -0.5 \, \text{N} \)

• Using Newton's second law \( F = ma \):
  • Mass \( m = 7.5 \, \text{kg} \)
  • Acceleration in the x-direction:
    • \( a_{x} = \frac{F_{x}}{m} = \frac{-10.67 \, \text{N}}{7.5 \, \text{kg}} = -1.42 \, \text{m/s}^2 \)
  • Acceleration in the y-direction:
    • \( a_{y} = \frac{F_{y}}{m} = \frac{-0.5 \, \text{N}}{7.5 \, \text{kg}} = -0.067 \, \text{m/s}^2 \)

Final Answer