Answer: a = 1.58 m/s²
Explanation: The mass of the object is 6.80kg.
From newton's second law of motion,
Resultant force = mass * acceleration
So we need to get the resultant force first.
Note all angles are measured from the positive x axis in the counter clockwise direction..
The first force is 10.10 N at an angle of 19° to the positive x axis.
Horizontal component of this force = 19× cos 19° =17.964 N
Vertical component of this force = 19 × sin 19° = 6.186N
The second force is 8.6 N, 122° ( 22° to the positive y axis), due to the angle, the force is between the positive y axis and negative x axis ( 2nd quadrant)
Horizontal component of this force = - 8.6×sin 22 = - 3.22 N
Vertical component of this force = 8.6 × cos 22 = 7.974 N
The third force is 9.8 N, 218° ( 38 degree to the negative axis), due to the angle, the force is placed in between the negative x and negative y axis.
Horizontal component of this force = - 9.8×cos 38 = - 7.722 N
Vertical component of this force = - 9.8 × sin 38 = - 6.033 N
Sum of forces on the x axis (fx) = 17.964 - 3.22 - 7.722 = 7.022 N
Sum of forces on the y axis (fy) = 6.186 + 7.974 - 6.033 = 8.127 N
Resultant force = √(fx) ²+(fy)²
Resultant force = √7.022² + 8.127²
Resultant force = √115.356613
Resultant force = 10.74 N
Recall that resultant force = mass * acceleration
10.74 = 6.8 × a
a = 10.74/6.8
a = 1.58 m/s²