Momentum = mass * speed
Speed is proportional to momentum; i.e. having twice the speed would result in double the momentum, a lower speed = smaller momentum, etc
Answer is d using a heavier string
So we want to know what is the magnitude of the horizontal component of acceleration ah if we know that the overall acceleration a=12 m/s^2 and the angle of overall acceleration and the horizontal acceleration is α=50°. We know that ah=a*cosα. So now it isn't hard to get the horizontal component: ah=12*cos50=12*0.64=7.71 m/s^2. So the correct answer is ah=7.71 m/s^2.
I think that the answer is 13.386 inches.
