Force X has a magnitude of 4 pounds and Force Y has a magnit

Force X has a magnitude of 4 pounds, and Force Y has a magnitude of 14 pounds. They act on a single point at an angle of 30degree to each other Answer the following questions. Treat Force X as a horizontal force. What is the magnitude of the resulting force? pounds (Do not round until the final answer. Then round to one decimal place as needed.) What is the directional angle of the resultant force? (Do not round until the final answer. Then round to one decimal place as needed.)

Solution

x=4,y=14,=30^o

x=4i

y=14cos30^oi +14sin30^oj=(73)i +(7)j

resultant vector =x+y

resultant vector=4i+(73)i +(7)j

reultant vector=(4+73)i +(7)j

magnitude of resultant vector=[(4+73)² +(7)²]

magnitude of resultant vector=[(4+73)² +(7)²]

magnitude of resultant force =17.6 pounds

directional angle=tan^-1[14sin30^o_{/[4+14cos30^o]}]

directional angle=tan^-1[7_/[4+73]]

directional angle=23.5^o