50 kg grandma is roller skating down the sidewalk at 2 m/s. Suddenly, someone throws her a 10 kg sack of oranges. How fast does she travel afterwards? (Inelastic)

v2 = 1.67m/s

she will travel at 1.67m/s afterwards

Explanation:

Given;

Mass of grandma m1 = 50kg

Mass of sack m2 = 10kg

Initial speed of grandma v1 = 2m/s

Final velocity of both = v2

The momentum equation of the initial and final momentum can be written as;

m1v1 = m1v2 + m2v2 = (m1+m2)v2

(Since the collision is inelastic they both move at the same velocity v2 after the collision)

making v2 the subject of formula;

v2 = (m1v1)/(m1+m2)

Substituting the values;

v2 = (50×2)/(50+10)

v2 = 1.67m/s

she will travel at 1.67m/s afterwards

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