<p>I am stuck on these problems, so please help me solve them (please also provide the steps so that I know how to do them later)
1. A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.00 m, 4.00 m) with a velocity of 5.00 m/s i(i vector) and an acceleration of +12.5 m/s2 j (j vector). What are the (a)x and (b)y coordinates of the center of the circular path?
2.Two ships, A and B, leave port at the same time. Ship A travels northwest at 24 knots and ship B travels at 28 knots in a direction 40° west of south. (1 knot = 1 nautical mile per hour=1.688ft/s) What are (a) the magnitude (in knots) and (b) direction (measured relative to east) of the velocity of ship A relative to B? (c) After how many hours will the ships be 160 nautical miles apart? (d) What will be the bearing of B (the direction of the position of B) relative to A at that time? (For your angles, takes east to be the positive x-direction, and north of east to be a positive angle. The angles are measured from -180 degrees to 180 degrees. Round your angles to the nearest degree.)
3. After flying for 15 min in a wind blowing 42 km/h at an angle of 20° south of east, an airplane pilot is over a town that is 55 km due north of the starting point. What is the speed of the airplane relative to the air, in km/h?</p>
<p>I wold gladly do these, but I've got 2 tests tomorrow >.<(which one of them ironically is in physics, and I need to solve more challenging problems to get ready) I'll do it tomorrow if you can wait that long.</p>
<p>Thank you for your response. These problems at due tomorrow morning at 11:30 am, so if you manage to do them before then, please help.</p>
<p>I got question #3 just a moment ago. I found the magnitude of velocity needed for the flight, then wrote the equation for the relative velocities. After that, I rewrote the equation for the velocity of plane with respect to the ground as its x and y components.</p>
<p>Unfortunately my first test is going to be from 8:30-10:30am -.-, since I'm assuming you have class by then I probably can't get a response fast enough.</p>
<p>These problems are actually due at noon, and I don't have a class until 1 pm. Please help.</p>
<p>Hahaha, the problems I encountered today were nothing at all like these, so alright.
1. Use a=v^2/r to find the radius, then construct a vector with a magnitude equal to the radius that's in the same direction as the acceleration vector (Since acceleration the acceleration vector and the radius are in the same direction)</p>
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<li>for a and b, draw a vector of length 28 in the direction of ship B, then starting from the tip of that vector, draw another vector of length 24 northwest, then add them using the tip-to-tail method. Then find the magnitude and directon of the resulting vector using trigonometry.</li>
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<p>2 (c) It's just distance/time=velocity, so use the magnitude of the velocity you found in a, then plug in 160 nautical miles for distance, and solve for time
(d) I'm guessing you'd have to use trig again for that. This time it's with respect to A not B so watch out.</p>
<p>the coordinates given (4, 4) are on the circle right, so I can use the distance formula to find the radius, right? I don't know how the velocity and acceleration vectors come into play.</p>
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<li>Just vectors and trig again. Draw the starting point, then draw the airplane 55 km north, and then from that point, draw a line 20° southeast of length 10.5 km (Because only 15 minutes of time was spent) From there, do tip-to-tail again and use trig to find the velocity vector of the plane. Don't worry about the units but remember to multiply the answer by 4 in the end because all this happened in 15 minutes, and we want the velocity in km/h</li>
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<p>Yes, they are on the circle, the acceleration vector is parallel to the radius. As I said, use a=v^2/r to find the radius</p>
<p>the due time has passed, but thank you anyway.</p>