Help: Physics Homework Problem

[shawonna23]

One afternoon, a couple walks five-eights of the way around a circular lake, the radius of which is 1.35km. They start at the west side of the lake and head due south to begin with.

a) What is the distance they travel?

b) What are the magnitude and direction (relative to due east) of the couple's displacement?

 

[kuenmao]

Somebody move this to the homework help zone...

I won't give you the answers, but I'll still give you some hints:

For (a), you have to calculate 5/8 of the circumference of the circular lake. The circumference length of any circle is 2*(pi)*(radius).
For (b), you have to draw a triangle inscribed in a circle, by joining the starting point, ending point and the centre of the circle. Then, you find out the angles and calculate the length of the line from the starting point to the ending point.

I hope that helped.

 

[PICsmith]

a) The distance is just 5/8 times the circumference, the formula for which will be in your book or easily found on the internet.

b) This is just a vector from where they started to where they ended up. Draw it out first as a circle centered at the origin, you know the distance from where they started to the origin is the same as the distance from the end to the origin, use pythagorum theorum to find the magnitude (length) of the vector. You can easily find the angle to find the direction.

edit: er, yeah what he said

 

[shawonna23]

I understand how to do part a, but I'm still having trouble understanding how to do part b. Can you show me how to do this in steps? Thanks!

 

[needhelpperson]

One afternoon, a couple walks five-eights of the way around a circular lake, the radius of which is 1.35km. They start at the west side of the lake and head due south to begin with.

a) What is the distance they travel?

b) What are the magnitude and direction (relative to due east) of the couple's displacement?

for part b: this is a little tricky, but you'll start to understand how to solve questions like these later on, once you have enough practice.

For convenience i'll use this formula to solve this question.
theta*radius = distance around a circle
theta= (5/8)*2pi

theta - pi= the angle between the vector and the x axis(in radians)

convert to degrees by (angle*180/pi)

You might want to draw the diagram out to help you understand. Now that you know theta, it's all simple trig from here on...