Answer:
The impulse is [tex]I= 0.1116\ kg \cdot m/s[/tex]
Explanation:
Generally Impulse which the change in momentum is mathematically represented as
[tex]I = m\Delta v[/tex]
Where m is the mass with a value 12.4g = [tex]\frac{12.4}{1000} = 12.4*10^{-3}kg[/tex]
[tex]\Delta v[/tex] is the change in velocity which is mathematically represented as
[tex]\Delta v = v_2 -v_1[/tex]
Where [tex]v_1[/tex] s the velocity of the marble drooping and [tex]v_2[/tex] is the velocity of the marble bouncing back
setting up in a coordinate y-axis would show that [tex]v_1[/tex] is moving in the negative y-direction so the value would be [tex]v_1 = -v_1[/tex] and [tex]v_2[/tex] is moving in the positive y-direction so the value would be [tex]v_2 = +v_2[/tex]
So the formula for [tex]\Delta v[/tex] would be
[tex]\Delta v = v_2 -( -v_1)[/tex]
[tex]\Delta v = v_1 +v_2[/tex]
General v i mathematically represented as
[tex]v = \sqrt{2gh}[/tex]
Substituting this into the formula for [tex]\Delta v[/tex]
[tex]\Delta v = \sqrt{2gh_2} + \sqrt{2gh_1}[/tex]
Now substituting values as given in the question
[tex]\Delta v = \sqrt{2 * 9.8 *0.614 } + \sqrt{2 * 9.8 *1.56 }[/tex]
[tex]= 8.9986 m/s[/tex]
The impulse is
[tex]I = 12.4*10^{-3} * 8.9986[/tex]
[tex]I= 0.1116\ kg \cdot m/s[/tex]
