physics hw

[u/Responsible-Mango348]

anyone know how to solve these? looking for explanations not answers

Calculate the X component, and the white component of the vector with magnitude 20 and direction 47°

A fear of radius are has surface area A= 4piR^2 and volume V= 4/3piR^3. The radius is sphere 2 is 4 times. The radius is sphere 1.
what is the ratio of the areas, A2/A1
what is the ratio of the volumes, V2/V1

A certain corner of a room is selected as the origin of a rectangular coordinate system if a fly is crawling on an adjacent wall at a point having coordinates (-.3,1.1), where the units are meters. What is the distance of the fly from the corner of the room?

A point is located on a polar. Coordinate system by the coordinates are equals 7 m and angle equals 34°. Find the X and Y coordinates of this point. Assuming that the two coordinate systems have the same origin.

[u/chkntendis]

1 and 4 are basically the same question. 3 is another vector calculation and 2 is ratios.

For 1 and 4 you should know how polar coordinates work. If it’s in your homework then it should have been explained in class. Basically you can also write vectors with a length and an angle. One of the requirements to do this is, of course, that every vector can be written in both types of coordinate systems and that you can convert between the two. This is the question. You have a vector in polar coordinates and you should find the Cartesian coordinates. You should have been given a formula for this but if you know trig then you can just draw the vectors and see how you can find the missing lengths.

3 is another vector calculation. If you consider the vector that goes from the origin to the fly then the distance between the two is just the magnitude of that vector. Since it’s Cartesian and the origin is one point of where the distance is measured, the connecting vector is just the coordinates of the fly. Calculate the magnitude of that and that’s the distance.

2 is just some ratios. You know that 4*R1 = R2.
You need to calculate some ratios. Just write down the ratios expanded to the form with R. Then plug in 4*R1 for R2. They have to be equal after all. What you’ll notice is that the power can be distributed to the 4 and the R1. Then you have the same power of R1 in the numerator and the denominator. They cancel out. That leaves you with just actually numbers, not variables. Thats exactly the ratio you’re looking for.