Calculations Involving Impulse
In the solution at the right, I started with the formula for impulse, which is impulse is equal to force x time. At this point in the class, we also know that impulse is equal to change in momentum, and so in the second line of the solution, I replaced impulse with final momentum - initial momentum. Then, in the third line of the solution, I solved for force (I got force all by itself on the right-hand side of the equation). In the fourth line of the solution, I replaced final momentum with mass x final velocity and initial momentum with mass x initial velocity. In the fifth line of the solution, I factored mass out of both terms on the top of the fraction in the left-hand side of the equation. Finally, I plugged in the values for the ball's mass, its final velocity (0 m/s because it stopped), the ball's initial momentum, and the time it took for your hand to stop the ball. In the end, we get the result that the net force exerted by your hand on the ball is equal to -50 Newtons. Note: It makes sense that the force is negative because, if the ball was initially moving in the positive direction, you had to exert a force on it in the negative direction to make it stop.