Three people pull simultaneously on a stubborn donkey. Jack pulls eastward with a force of 64.7 N, Jill pulls with 61.5 N in the northeast direction, and Jane pulls to the southeast with 171 N. (Since the donkey is involved with such uncoordinated people, who can blame it for being stubborn?) Find the magnitude of the net force the people exert on the donkey. What is the direction of the net force? Express this as the angle from the east direction between 0.

F = 241.8 N θ = - 18.7

Explanation:

To find the net force, we use Newton's second law, for this we decompose the force using trigonomer

Force 2

F2 = 61.5 N

cos 45 = F₂ₓ / F2 F₂ₓ = F2 cos 45

sin 45 = F₂_y / F2 F₂_y = F2 sin 45

force 3

F3 = 171 N

cos 45 = F₃ₓ / F3

sin 45 = F₃_y / F3

the total force can be found with its components

axis x direction (East-West)

Fₓ = 64.7 + 61.5 cos 45 + 171 cos 45

Fₓ = 229.1 N

Y axis (direction North - Sur)

F_y = 61.5 sin 45 - 171 sin 45

F_y = - 77,428 N

the resulting force is

F = Fx i ^ + Fy j ^

F = (229.1 i⁻ 77,428 j⁾ N

we can use the Pythagorean theorem to find the module

F = √ (229.1 2 + 77,428 2)

F = 241.8 N

let's use trigonometry to find the direction

tan θ = F_y / Fₓ

θ = tan⁻¹ (F_y / Fₓ)

θ = tan⁻¹ (-77,428 / 229.1)

θ = - 18.7