which of the following equations would be best to use?

Question

A 0.1kg ball falls 3.2m, reaching a speed of 8 m/s. At this point it strikes a surface, exerts an average force of 10N, rebounds with a speed of 6 m/s and reaches a height of 1.8m. To find the time during which the ball was in contact with the surface, which of the following equations would be best to use?
• change in potential energy stored = mass x gravitational field strength x distance
• force x time = momentum change
• change in kinetic energy stored = ½ mass x (final speed² - initial speed²)
• final speed = initial speed + (acceleration x time)
• distance = (initial speed x time) + (½ acceleration x time²)

Answer 1

Lets try Momentum. This problem involves a collision that has impulse energy after hitting the ground. This impulse changes the Momentum, ∇M =  ∫Fdt = F*∇t  it is known as an impulse with an average force F over the time ∇t. It is important to always note that Momentum is a vector while energy is a scalar quantity. It took some hundred years to understand this difference. Assume positive up negative down. The Momentum due to the change in velocity is m*(v1-v2) and from the impulsive force is N*∇t. From the conservation of Momentum

M*(v1-v2)=N*∇t.  Using conservation of Momentum the problem gives 0.1*(8-(-6)) = 10*∇t giving ∇t = .14 sec. The units are kg*m/sec=newton-sec. Velocity v1 is 8m/sec pos down and v2 is -6 m/sec neg up. The force creates a positive impulse N-sec to increase the Momentum.  

Answer 2

force x time = momentum change