In this problem, a person pushes a 16 Katie shopping cart at a constant velocity for a distance of 16 m. She pushes a direction 25° below the horizontal. At 42. Newton fractional horse opposes the motion of bye. Okay, so it is us. That what is the magnitude of the force this shop? The person shopper exert straight the shopper exit on the shopping cart. Right? So we need to determine the work done by the pushing fools, right? And they can be disaster work done by frictional force. And we are asked to find it. Work turned by reputational force. Yes, So this is all about angles making with pushing force, frictional force, and gravitational force. Right? So we are just calculating for it. So here on applying Newton's second law of motion, we know that Net Force is a mission of f equals two. Of course 25 minus if he goes to zero. Right? So this will give us upon F Small left by past 20 five. So we're small air is what? Small service. 42, New Daniel. Okay, so this will give us 42 divided by two. Was 25. This will hear us What is six Yeah, today forward, you know, So this is it answered. Okay, now, for the second part, work done by pushing force will be equals two. Okay, W one FD W one equals two. FD cost 25. So 42 into 16 cost 25 with the word. So he and legacy for 25. Engine 16 and 3016. There to play 16 to what you do. Engine boss 25 great. So this is going to be risk 609 16. 609 0.3 plane then this is this is all Jr together. Yes. So they should win and you expect this is it. And right for the C. Part work done by the by the frictional forces, work done by the frictional force will be it was too W It was two FD because one intuitively, you know that the angle between them is one degree. We know that if it is an object then if if it is moving in this within frictional forces acting this week with the angle will be went into Disney like. Mhm. So here we can see We can say 42 into 16. This will give us minus 600 72. I'm sorry, I need to correct here somewhere. Uh this is absolute pushing forces. You see the the angle is zero taking the year. So this will give us mhm 4240 is 1 42- 16 years. Six 70 two. Yeah, late. And We are getting by 6 72. Were done by original courses. So, these forces are pushing and pulling forces. Are You put an opposing the artist pushing one is 673 two and French forces -670 two. Right, so now last for the last one. Love done by gravity will be equal to F. D. Cost like right. So they should be Indeed, they should be MD by engine 20. That is zero, joe. It's great. So, this is an answer. I hope you understand. This is how we solve this problem. Thank you for watching.