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Problem 12 Easy Difficulty

At an instant when a soccer ball is in contact with the foot of a player kicking it, the horizontal or $x$ component of the ball's acceleration is 810 $\mathrm{m} / \mathrm{s}^{2}$ and the vertical or $y$ component of its acceleration is 1100 $\mathrm{m} / \mathrm{s}^{2}$ . The ball's mass is 0.43 $\mathrm{kg}$ . What is the magnitude of the net force acting on the soccer ball at this instant?

Answer

590$N$

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Video Transcript

So this question we have to calculate what is the magnitude of acceleration. So then we can use Newton's second law to determine what is the magnitude of the resulting force. So how can he calculates the magnitude off acceleration? Well, we have to make a vector addition this vector plus the factor. What is the result? Well, let me do a drawing. We have one vector that points on the result. All access. And then I have another back toward that points on the vertical axis. As a rule off adding vectors, we put the end off one vector on the beginning. Off the other factor, Sir, we will put the end off these actor on the beginning off. These one the result of the following. Okay, now we have a wine here and a X here. What is the resulting factor from these addition? It is these one, okay? And this is the resulting acceleration knows that this is a rectangle triangle. This is a 90 degree angle. Better form. It is true by using the category in fear, um, that a squared is equal to a X squared plus y squared under for a easy cause to the square root off a X squared plus y squared. Then we can played in their values that were given by the problem to calculate the magnitude off the resulting acceleration and is the following A is equal to the square it off 810 squared +11 double zero squared and this gives us approximately 13 66 meters per second squared. So this is the resulting inspiration. I get points in between to accelerations, so it points in this direction and the magnitude is approximately 1366 meters per second squared. Now, in order to complete the magnitude off the force that is active in the ball, we use Newton's second law. It says that the resulting force is it goes to man. It's time that exploration off the boat. But this is the vector form off neutral. Second look As we are interested in the magnitudes, then we use the magnitude off the result in force which is not the vector and the magnitude of text relation. The magnitudes are not factors their numbers so we can operate them as usual. So the magnitude off the resulting force is the mass times the magnitude off the resulting incineration. Then we have the following. The mining turned off. The resulting force is a question zero point for tree times 1366 and this gives us a resulting force off approximately 508 7 new tunes.