Question

Two forces act at right angles at a point on a body. One of the forces is 120 lb. and the other is 160 lb. Find the magnitude of the resultant of the two forces.

Answer 1

Hello!

The answer is: The resultant force is equal to 200 lb.

Why?

From the statement, we know that both forces are acting at right angles, meaning that there is a vertical force and a horizontal force.

We can solve this problem using the Pythagorean Theorem, which states that:

$c^{2}=a^{2}+b^{2}$

Let be:

a, the horizontal force (x)

b, the vertical force (y)

c, the resultant force (r)

So, assuming that:

$x=120lb\\y=160lb$

Calculating the resultant force, we have:

$r^{2}=x^{2}+y^{2}=(120lb)^{2}+(160lb)^{2}\\\\r^{2}=(120lb)^{2}+(160lb)^{2}=14400lb^{2}  +25600lb^{2} =40000lb^{2}\\\\r^{2}=40000lb^{2} \\\\r=\sqrt{40000lb^{2} }=200lb$

Hence, the resultant force is equal to 200 lb.

Have a nice day!

Answer 2

Answer: The resultant force is equal to 200 lb.