I'm confused, and I can't seem to get this question right. someone please help. Only two forces act on an object (mass = 5.00 kg), as in the drawing. (F = 55.0 N.) Find the magnitude and direction (relative to the x axis) of the acceleration of the object. (Drawing: 45 degrees, Fx is 40 N)

17.6 m/s², 26.2° above x axis

Explanation:

Apply Newton's second law.

Sum of forces in the x direction:

∑Fₓ = ma

40 N + 55.0 N cos 45° = (5.00 kg) aₓ

aₓ = 15.8 m/s²

Sum of forces in the y direction:

∑Fᵧ = ma

55.0 N sin 45° = (5.00 kg) aᵧ

aᵧ = 7.78 m/s²

Use Pythagorean theorem to find the magnitude of the resultant.

a² = aₓ² + aᵧ²

a² = (15.8 m/s²)² + (7.78 m/s²)²

a = 17.6 m/s²

Use trigonometry to find the angle.

tan θ = aᵧ / aₓ

tan θ = (7.78 m/s²) / (15.8 m/s²)

θ = 26.2°

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