A bar of soap (mass 0.1 kg) is sliding at 1.5 m/s, before smashing into a motionless bar of soap (mass 0.08 kg). After hitting each other, the soap sticks together and continues to slid. Ignore friction. what is the velocity of bars of soap after sticking together?

5/6 = 0.833

Explanation:

From conservation of momentum,

m1*u1  + m2*u2 =  (m1+m2)*v

v = (m1*u1 + m2*u2)/(m1*m2)

Putting in the values, we get, v = 5/6 = 0.833

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