Question

7. Jake is bowling with a 8 kg bowling ball. He rolls the ball at 7 m/s, and it hits one stationary pin with a mass of 2 kg. The pin goes flying forward at 12 m/s. How fast is the bowling ball now traveling?

Answer 1

This is a conservation of momentum problem. Initial momentum must equal final momentum. 
Momentum= mass* velecoity
I will denote Ball as b and pin as p
Initial momentum= V(initial b)* Mass(b)+ V(initial p) *mass (p)
since the pin is stationary to begin that means velocity is 0 and we can plug in for the rest
Initial momentum= 7m/s*8kg=56 mkg/s
Now for final momentum=V(final b)*mass(b)+V(final p)*mass(p) plugin
final momentum=V(final b)*8kg+12m/s*2kg
we can set final momentum= inital momentum and solve for V(final b)
56mkg/s= V(final b)*8kg+ 24mkg/s
32mkg/s=V(final b)*8kg
4m/s=V(final b)
so 4 meters/second is the answer