Question

What is the net force on a remote controlled airplane if a force of 57.6N is applied West and a force of 95.7N is applied South?

Answer 1

112 N at 239°

Step-by-step explanation:

Applying,

Pythagoras theorem,

a² = b²+c².................. Equation 1

Where a = net force

From the question,

Given: b = 57.6 N, c = 95.7 N

Substitute into equation 1

a² = 57.6²+95.7²

a² = 3317.76+9158.49

a² = 12476.25

a = √12476.25

a = 111.7 N

a ≈ 112 N

Then the direction is given as

∅ = tan⁻¹(c/b)........... Equation 2

∅ = tan⁻¹(95.7/57.6)

∅ = tan⁻¹(1.66)

∅ = 58.9°

∅ ≈ 59°

Since the angle is in the third quadrant,

∅' = 59+180

∅ = 239°

Hence the right answer is

112 N at 239°