A block has two forces on it. One force is 15 N going north and the other is 22 N going east. What is the overall force pushing on the block with magnitude and direction?

The overall force pushing on the block is 26.63 N in the direction of N 34° E

Explanation:

Given;

force going north, F₁ = 15 N

force going east, F₂ = 22 N

The resultant of the two forces is the hypotenuse side of the right angled triangle formed by the two forces.

Let the magnitude of the resultant force = F

F² = F₁² + F₂²

F = √(F₁² + F₂²)

F = √(15² + 22²)

F = 26.63 N

The direction of the force is the angle between the resultant force and the horizontal force.

tan θ = 15 / 22

tan θ = 0.6818

θ = tan⁻¹ ( 0.6818)

θ = 34°

Therefore, the overall force pushing on the block is 26.63 N in the direction of N 34° E

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