Question

Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 1

might want to divvy up the angles into xy parts such that: x = rcos(t) and y = rsin(t)

Answer 2

personally, i would negate the 100 by 30 vector and add it to the other one

Answer 3

i have still no clue how to solve this problem..

Answer 4

:) we could go a longer route; find the up and over forces and compare them

for the 30 by 100 vector, x = 30 cos(100). y = 30sin(100)
for the 25 by 10 vector, x = 25 cos(10). y = 25sin(10)

the net values of the x and y parts will equate to the resultant vector components and force

Answer 5

so resultant is equal to the sum of the forces in the given x and y directions

x = 30 cos(100). y = 30sin(100)
x = 25 cos(10). y = 25sin(10)

Rx = 30cos(100) + 25cos(100)
Ry = 30sin(10) + 25sin(10)

Answer 6

the angle would then be the arctangent of Rx/Ry

Answer 7

the angle would then be the arctangent of Ry/Rx

Answer 8

and the force is the "length" of the vector: F = sqrt(Rx^2+Ry^2)

Answer 9

so when i find F i get my answer?

Answer 10

Find the direction AND magnitude
arctan(Ry/Rx) sqrt(Rx^2+Ry^2)

Answer 11

okat thank you veryy much! :)

Answer 12

direction is: http://www.wolframalpha.com/input/?i=arctan%28+%2830sin%28100%29%2B25sin%2810%29%29%2F%2830cos%28100%29%2B25cos%2810%29%29%29

force is: http://www.wolframalpha.com/input/?i=sqrt%28%2830sin%28100%29%2B25sin%2810%29%29%5E2%2B%2830cos%28100%29%2B25cos%2810%29%29%5E2%29

:)