Question

Can someone please help me with this problem?
Nancy & Harry are lifting a stone statue and moving it to a new location in their garden. Nancy is pushing the statue with a force of 120 newtons (N) at a 60 degree angle with the horizontal while Harry is pulling the statue with a force of 180 N at a 40 degree angle with the horizontal. What is the magnitude of the combined force they exert on the statue? Round answer to the nearest hundredth.

Answer 1

Drawing will help.

Answer 2

I've tried, it confuses me even more because I don't know what I'm doing and if I'm doing it right.

Answer 3

One way to do it is by x and y components.

Answer 4

Thank you for giving me an illustration :)

Answer 5

120-N force at 60 deg:
x-component: 120*cos(60)
y-component: 120*sin(60)

180-N force at 40 deg:
x-compnent: 180*cos(40)
y-component: 180*sin(40)

Resultant's sum of components:
x-component: 120*cos(60) + 180*cos(40) = 60 + 137.888 = 197.888
y-component: 120*sin(60) + 180*sin(40) = 103.923 + 115.702 = 219.625

Answer 6

R = sqrt(197.888^2 + 219.625^2) =
R = 288.781
Angle = tan^-1(219.625/197.888) = 47.98 deg

Answer: 289 N at 48.0 deg