Respuesta :
Answer: 1280.63 N, 231.35°
Explanation: Both the vertical and horizontal force are perpendicular to each other.
The horizontal force is 800 N to the back ( which corresponds to a force of 800 N acting in the negative x direction).
The vertical force is 1000 N acting down vertically against the ground ( which corresponds to a force of 1000 N acting in the negative y direction)
Hence the resultant force is placed in the third quadrant ( between the negative x and negative y axis).
The magnitude of resultant force is gotten below as
R = √(Fx)² + (Fy)2
Fx = 800 and Fy = 1000 N
R = √800² + 1000²
R = √640000 + 1000000
R =√1640000 = 1280.63 N
direction = tan^-1 ( 1000/800) = tan^-1 (1.25) = 51. 35°
But the force is on the third quadrant, hence angle is 180 + 51.35° = 231.35°
The magnitude and direction of the resulting vector is 1280.63 N and 231.35° respectively.
The magnitude of resultant force can be calculated by
R = √(Fx)² + (Fy)²
Where,
Fx - Force in X-axis = 800 N
Fy = Force in Y- axis = 1000 N
Put the values in the formula,
R = √800² + 1000²
R = √640000 + 1000000
R =√1640000 =
R = 1280.63 N
The direction of resulting vector can be calculated by
[tex]\bold {\theta = tan^{-1} \dfrac {1000}{800} }\\\\\bold {\theta = tan^{-1} (1.25)}\\\\\bold {\theta = 51. 35°}[/tex]
But the force is on the third quadrant, is 180
Hence Direction,
= 180 + 51.35° = 231.35°
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