Determine the centre of mass coordinatesof a system of two objects of masses 3.0 kgand 15 kg, respectively, kept at a distanceof 2.0 m from one another.

To determine the center of mass coordinates of a system of two objects, we can use the formula:

x_cm = (m1x1 + m2x2) / (m1 + m2) y_cm = (m1y1 + m2y2) / (m1 + m2)

where m1 and m2 are the masses of the objects, (x1, y1) are the coordinates of the first object, and (x2, y2) are the coordinates of the second object.

In this case, we have two objects with masses of 3.0 kg and 15 kg, respectively, and they are kept at a distance of 2.0 m from each other.

Let's assume that the first object is located at coordinates (0, 0) and the second object is located at coordinates (2.0, 0).

Using the formula, we can calculate the center of mass coordinates:

x_cm = (3.0 kg * 0 + 15 kg * 2.0) / (3.0 kg + 15 kg) = 30 kgm / 18 kg = 1.67 m y_cm = (3.0 kg * 0 + 15 kg * 0) / (3.0 kg + 15 kg) = 0 kgm / 18 kg = 0 m

Therefore, the center of mass coordinates of the system of two objects are (1.67 m, 0 m).