Two people push on a 4 kg object. One force is 60N, north. The second force is 40N, east. Find the acceleration of the object. Ignore friction. The answer is 18m/s/s at 53.31 degrees.......but i don't know how to get to it.

Add the two forces to get the resultant force. Since they are at right angles,

the magnitude |F| is sqrt[60^2 + 40^2] = 72.11 N
The accleration is F/m = 18.02 m/s^2

The direction of the accleration is the direction of the resultant force, which you should be able to get from the ratio of the two forces (which is an arctangent of the angle from one axis)

To find the acceleration of the object, we can use Newton's second law of motion, which states that the force applied on an object is equal to the mass of the object multiplied by its acceleration.

First, let's break down the forces applied on the object into their horizontal (x) and vertical (y) components.

The force of 60N, north is in the y-direction (upwards), and the force of 40N, east is in the x-direction (rightwards).

Now, let's calculate the net force in the x and y directions. Since there is no friction, the net force in each direction is equal to the sum of the forces in that direction.

In the x-direction, the net force is the force applied in the x-direction, which is 40N, east.

In the y-direction, the net force is the force applied in the y-direction, which is 60N, north.

Next, we need to calculate the acceleration in each direction. Recall that acceleration is the rate of change of velocity, and velocity is the rate of change of displacement. Since the displacement is usually measured along x and y axes separately, we need to calculate the acceleration in each direction.

Using Newton's second law, we know that F = ma, where F is the net force, m is the mass, and a is the acceleration.

In the x-direction, the net force is 40N, east, and the mass is 4 kg. Therefore, the acceleration in the x-direction can be calculated as follows:

40N = 4kg * ax
ax = 40N / 4kg = 10 m/s² (east)

In the y-direction, the net force is 60N, north, and the mass is 4 kg. Therefore, the acceleration in the y-direction can be calculated as follows:

60N = 4kg * ay
ay = 60N / 4kg = 15 m/s² (north)

Finally, we can find the resultant acceleration of the object using the Pythagorean theorem. The resultant acceleration magnitude can be calculated as follows:

|a| = √(ax² + ay²) = √((10 m/s²)² + (15 m/s²)²) ≈ 18 m/s²

To find the direction of the resultant acceleration, we can use trigonometry. The angle θ can be calculated as follows:

θ = arctan(ay / ax) = arctan(15 m/s² / 10 m/s²) ≈ 53.13°

Therefore, the acceleration of the object is approximately 18 m/s² at an angle of 53.13° north of the positive x-axis.