momentum problems finding velocity.. please help me?

Question

# 4 a stationary .14kg ball is struck by a .23 kg ball moving east at 2 ms. After the collision, the .14kg ball has a velocity of .9m/s at a 30 degree angle. What is the velocity of the .23kg ball?

#5. A .50kg ball at rest is struck by a .30kg ball moving west at 5m/s. After the collision, the .30kg ball has a velocity of 3m/s, 200 degree angle. What is the velocity of the .50kg ball?

#6 a 2kg object moves at 4 m/s south. It strikes a 3 kg object at rest. After the collision, the 2kg object has a velocity of 2.5 m/s at a 300 degree angle. What is the velocity of the 3kg object?

please help me

Answer 1

#4
.23*2=.23*v*cos((θ)+.14*.9*cos(30)
and
.23*v*sin(θ)=0.14*.9*sin(30)
solve for v

.23*2-.14*.9*cos(30)=.23*v*cos((θ)

divide
tan(θ)= 0.14*.9*sin(30)/(.23*2-.14*.9*cos(30))
θ=10.18 degrees
v=1.55 m/s

#5
.3*5=.3*3*cos(20)+.5*v*cos(θ)
.3*3*sin(20)=.5*v*sin(θ)
solve for v

.3*5-.3*3*cos(20)=.5*v*cos(θ)

tan(θ)=.3*3*sin(20)/
(.3*5-.3*3*cos(20))

v=1.445 m/s
which is North West at an angle of 25.2 degrees above horizontal, or 154.8 degrees

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