You find a job as part of a team doing oceanic research. the team is going to monitor water temperature, salinity, ph, etc. to do this, the team is going to use an instrument package contained in a hollow, aluminum sphere. the aluminum sphere has an outer diameter of 1.00 m and a thickness of 1.00 mm·(use 2.70 g/cc for the density of the aluminum) the aluminum sphere will be supported by a tether connected to a solid styrofoam sphere that is also of 1.00 m diameter. (use 300.0 kg/m3 for the density of styrofoam)

a) your task is calculate the maximum weight that the instrument package can be without the whole thing sinking.
b) the team cannot change the size of the spheres or the material they are made of, but what suggestion can you make that would increase the maximum possible weight of the instrument package?

    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s