Solving Vector Problems: A+B+unkC = (15,0)

[Miike012]

Check out picture for problem...

My solution:

Vector pointing towards girl: I named it vector A, Boy Vector B

R = A + B + unkC = (15,0)

A = Ax + Ay = (10,0)
B = Bx + By = (0,5)
C = Cx + Cy = (?,?)

Total = 10,5
Cx = 5 Cy = -5

(50)^(1/2) = 7 = C

The answer however was 14

 

[quietrain]

erm ,

this is how to think

if you want the resultant of forces A B C to be 15 upwards, then that means your total horizontal forces are 0 , while your total vertical forces = 15 upwards

since your current set-up has 10 to the right and 5 to the top, this means that you need 10 to the left to make your total horizontal forces are 0. likewise, you need 10 to the top so that total total vertical forces = 10+5 = 15 upwards

so your "additional force C" comprise of 10 to the left and 10 to the top, which means the resultant of C is

C² = 10² + 10²
C = 14.1 N , directed diagonally to the top-left direction

 

[quietrain]

oh, in case you want to put it mathematically, it will be something like this

take right and upwards direction as positive,

solving for x-components,

total x = B + C_x = 0
+10 + C_x = 0
C_x= -10 , this tells you C_x is directed to the left, because we took right as positive

solving for y-components,

total y = A + C_y = 15
5 + C_y = 15
C_y = +10, this tells you C_y is directed upwards , because we took upwards as positive

so resultant C² = C_x² + C_y² --> pythagoras theorem

so C = 14.1

for direction, if we take angle T to be between the x-axis and the resultant C, then

tan(T) = C_y / C_x = 10/10 =1
thus, T = 45 degrees

 

[Miike012]

Thank you!