Find the magnitude and direction of the resultant force produced by a vertically upward force of 42 N and a left horizontal force of 35N.

Resultant = 54.67 N

Direction: 50.2° to the horizontal

Explanation:

Note: Since both forces form a right angle triangle, As shown in the diagram below,

Applying

Pythagoras theorem,

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

From the question,

a = R, b = 42 N, c = 35 N

Substitute these values into equation 1

R² = 42²+35²

R² = 1764+1225

R² = 2989

R = √2989

R = 54.67 N

Direction

tanФ = a/b

Where Ф = direction of the resultant

tanФ = 42/35

tanФ = 1.2

Ф = tan⁻¹(1.2)

Ф = 50.2° to the horizontal