Question

A worker pushes a large rock to the north while another worker helps by pushing it to the east. If they both exert equal force, in what direction does the rock move?

Question 2 options:

northeast

east

north

southwest

Answer 1

let the magnitude of force applied by each worker be "F"

consider east-west direction along X-axis and north-south direction along Y-axis

In unit vector form, force vector by worker pushing in east direction is given as

`\underset{A}{\rightarrow}` = F
`\hat{i}` + 0
`\hat{j}`

In unit vector form, force vector by worker pushing in north direction is given as

`\underset{B}{\rightarrow}` = 0
`\hat{i}` + F
`\hat{j}`

resultant force is given as the vector sum of two vector forces as

`\underset{R}{\rightarrow}` =
`\underset{A}{\rightarrow}` +
`\underset{B}{\rightarrow}`

`\underset{R}{\rightarrow}` = (F
`\hat{i}` + 0
`\hat{j}` ) + (0
`\hat{i}` + F
`\hat{j}` )

`\underset{R}{\rightarrow}` = F
`\hat{i}` + F
`\hat{j}`

direction of the force is hence given as

θ = tan⁻¹(F/F)

θ = tan⁻¹(1)

θ = 45 degree north of east

hence the direction is north-east