Whenever I visit one of the big membership-driven bulk wholesalers in town, without fail I end up using a junk cart with bum wheels that not only drag, but pull to the left. If a cart requires 20 lb of force forward to overcome the wheel’s drag, but there are also around 3 lb of force pulling it to the left, with what force and in what direction do I need to push in order to make the cart go forward? Required:
Measure your angle from the forward direction and specify whether it’s to the left or right.

Force of magnitude 20.22lbf to the right at angle 8.5°

Explanation: The image named "Untitled" below shows the forces acting on the cart.

The second image, "Untitled2", demonstrate the vector diagram of the forces acting on the kart, in which:

f is force forward

f(left) is pull to the left

f(R) is the resulting force necessary for the kart to move

The drag force is not draw on the vector diagram because its value is already part of the force forward.

As we can see, the diagram forms a right triangle with f(R) as hypotenuse.

Using Pytagorean Theorem:

f(R) = 20.22

Force forward equals 20.22lbf to the right.

The angle formed form the forward direction and the resulting force is

cosθ = 0.989

θ = cos⁻¹(0.989)

θ = 8.5°

The forward force is to the right at angle 8.5° and magnitude 20.22lbf.

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.