Two carts of identical mass (500 kg). One is traveling south and the other is traveling east. They collide (inelastic collision) and slide 3 meters, 30 degrees south of the east. The total friction force is 10,000N. Calculate the initial velocities of each.

Answer 1

The law of conservation of linear momentum for the inelastic collision
x: m1•v1=(m1+m2) •v• cos30°
y: m2•v2=(m1+m2) •v• sin30°
v1=2•v• cos30°
v2=2•v• sin30°

(m1+m2) •a=F(fr)
a= F(fr)/(m1+m2)=F(fr)/2m=10000/2•500=10m/s²
s=v²/2a =>
v=sqrt(2•a•s)=sqrt (2•10•3)=7.75 m/s.
v1=2•v• cos30°=2•7.75 •cos30°=13.42 m/s
v2= 2•v• sin30°=2•7.75 •sin30°=7.75 m/s