Total distance walked????

Question

1. Two boys push on a box. One pushes with a force of 125 N to the east. The other exerts a force of 165 N to the North. What is the size and direction of the resultant force on the box?

2. An explorer walks 13 km due east, then 18 km north, and finally 3 km west.

a. What is the total distance walked?

b.What is the resulting displacement of the explorer from the starting point?

i know the formula...

but it seems that it didn't match....

hope you can help me....

thanks in advance.....

Answer 1

1. Use the Pythagorean theorem. size = sqrt(125² + 165²) which is about 207 N, direction = arctan(165/125) which is about 52.85 degrees north of east

2.

a. 13 + 18 + 3 = 34 km

b. sqrt(10² + 18²) = about 20.59 km

Answer 2

The force (125, 165) has a magnitude of sqrt(125² + 165²) ~= 207 N. It points at atan(125 / 165) ~= 37 degrees away from North, in the East direction (or, if you prefer, it points 8 degrees north of pure-northeast.)

2.

a. 18 + 13 + 3 km. Distance is always the absolute length someone has traveled.

b. Well, if he was close to the poles, that's a hard question. But otherwise, he traveled from (0,0) to (10, 18) km.

Answer 3

1. Two boys push on a box. One pushes with a force of 125 N to the east. The other exerts a force of 165 N to the North. What is the size and direction of the resultant force on the box?

Call east angle of 0 and positive angles CCW from there.

F1 = 125 ∠0

F1x = 125

F1y = 0

F2 = 165 ∠90

F2x = 0

F2y = 165

add by adding the x and y components.

Fx = 125

Fy = 165

magn F = √(125² +165²) = 207

angle F = arctan 165/125 = 52.8 deg

2. An explorer walks 13 km due east, then 18 km north, and finally 3 km west.

a. What is the total distance walked?

13+18+3 = 34 km

b.What is the resulting displacement of the explorer from the starting point?

if you draw it, you see that the displacement is 10E and 18N

d = √(10² +18²) = 20.6 km

edit: do not depend on formula. You notice I did not use any formula, just my common sense and experience.

.