Assume that the origin goes through the place marked in the diagram. The three masses are connected by massless, rigid rods of 30 cm length (center-to-center). If the mass of A is 100 g, the mass of B is 150 g and the mass of C is 400 g, what is the x-coordinate (in cm) of the center of mass? What is the y-coordinate (in cm) of the center of mass?

In the figure below, the masses of each object are: m₁ 1.00 kg, m₂ = 4.00 kg, m² = 6.00 kg. The labeled distances are: d₁ = 25.0 cm, d₂ = 104 cm, d3 = 60.0 cm (where d is the x distance for the center of the block). The height of each block is h₁ = 19.0,h₂ = 28.0 cm, and the h3 = 12.0 cm. Assume the center of mass for each individual object is at the center of the object. Hint: Consider the final center of mass (x,y) relative to the axes shown in the figure. Note the positions of the boxes relative to the axes and to one another. Determine the positions, x and y, of the center of mass for the system below. Enter to 3 significant figures Center of mass (x, y): ( d1 m1 d3 d2 h1 ✔cm = m3 m2 h2 ✔ cm) 11h3 X

An astronaut floating at rest in space has run out of fuel in her jetpack. She realizes that throwing tools from her toolkit in the opposite direction will help propel her back toward the space station. If the astronaut has a mass of 85 kg and she throws a hammer of mass 4.5 kg at a speed of 4 m/s, what will be the approximate resultant velocity that carries her back to the space station?

Two cars are driving in the same direction separated by 220 m. The car in front has a mass of 1500 kg and is moving at 22 m/s. The car in the back has a mass of 1200 kg and is moving in the same direction at 15 m/s. Part A: How far ahead of the trailing car is the center of mass? Part B: What is the velocity of the center of mass? (if the center of mass is moving opposite the direction the cars are moving, indicate with a negative sign) Part C: What is the total momentum of the two-car system? (if the system momentum is opposite the direction that the cars are moving, indicate with a negative sign)