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