An object of mass 10 kg is traveling with a constant velocity of 5 m/s over a frictionless surface. This mass then begins traveling over a rough surface that does contain friction. If the mass loses 50 J of
energy, determine the final velocity of the mass.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

3. dark matter

empty space could also be a simple vacuum