Question

A child pulls a wagon with a force of 31 lbs. The handle of the wagon makes a angle of 45 with the ground. Express the force vector F in terms i and j.

Answer 1

To express the force vector F in terms of the unit vectors i and j, we need to break down the force into its horizontal and vertical components.

Given that the child pulls the wagon with a force of 31 lbs at an angle of 45 degrees with the ground, we can determine the horizontal and vertical components of the force as follows:

Horizontal component: Fx = F * cos(θ)
Vertical component: Fy = F * sin(θ)

Where:
F is the magnitude of the force (31 lbs)
θ is the angle between the force and the ground (45 degrees)

Substituting the given values into the equations, we have:

Fx = 31 lbs * cos(45°)
Fy = 31 lbs * sin(45°)

Using the approximation values for cosine and sine of 45 degrees:

Fx ≈ 31 lbs * 0.7071
Fy ≈ 31 lbs * 0.7071

Simplifying:

Fx ≈ 21.92 lbs
Fy ≈ 21.92 lbs

Therefore, the force vector F can be expressed as:

F ≈ 21.92 lbs * i + 21.92 lbs * j