Question

A force of 50 pounds acts on an object at an angle of 45 degrees. A second force of 75 pounds acts on the object at an angle of -30 degrees. Find the direction and magnitude of the resultant force.

Answer 1

Answer:

The magnitude of the resultant force is:

$R=100.3 \:pound$

The direction is:

$\theta=1.2^{\circ}$

Step-by-step explanation:

Let's find the components of each vector is x and y-directions first.

Sum of x-component vector forces.

$F_{tot-x}=F_{1}cos(45)+F_{2}cos(30)$

$F_{tot-x}=50cos(45)+75cos(30)$

$F_{tot-x}=100.3 \: pound$

Sum of y-component vector forces.

$F_{tot-y}=-F_{1}sin(45)+F_{2}sin(30)$

$F_{tot-y}=-50sin(45)+75sin(30)$

$F_{tot-y}=2.1 \: pound$  

The magnitude of the resultant force is:

$R=\sqrt{100.3^{2}+2.1^{2}}$

$R=100.3 \:pound$

The direction is:

$tan(\theta)=\frac{2.1}{100.3}$

$\theta=arctan(\frac{2.1}{100.3})$

$\theta=1.2^{\circ}$

I hope it helps you!