Answer:
A) ΔP = 4.5 [kg*m/s]
B) F = 375 [N]
Explanation:
The linear momentum is defined as the product of the mass of a body by Velocity, therefore we must calculate the momentum for each case.
[tex]P = m*v[/tex]
where:
P = linear momentum [kg*m/s]
m = mass [kg]
v = velocity [m/s]
A)
When the soccer ball is rolling towards the player
[tex]P =0.25*6\\P = 1.5[kg*\frac{m}{s}][/tex]
After kicking the ball
[tex]P = 0.25*24\\P = 6 [kg*\frac{m}{s} ][/tex]
Therefore the change  momentum is equal to
ΔP = 6 - 1.5 = 4.5 [kg*m/s]
B) Momentum is defined as the force applied for a certain time, this momentum produces a linear momentum.
We must be especially careful in the directions of the movement, since depending on the direction a positive or negative sign must be included according to the established convention. In this particular case we are going to take the kick and the direction of this as positive, that is to say, the ball moves in the negative direction and after hitting the ball it moves in a positive direction.
[tex]-(m*v_{1}) + F*t = (m*v_{2})\\-(0.25*6) + (F*0.02) = (.25*24)\\F*0.02= (7.5)\\F = 375 [N][/tex]
