Two girls pull on a cart. One pulls with a force of 25 N, the other with a force...

Question

Two girls pull on a cart. One pulls with a force of 25 N, the other with a force of 16
N. In what relative directions can the girls act to give the cart the smallest
acceleration? (Answer: Pull in the opposite direction will give the smallest
acceleration…show your work to come up with this answer)

Answer 1

Using the Law of Cosines:

c² = a² + b² - 2ab cos θ

The minimum value exists at cos θ = 1, or θ = 0

The minimum acceleration is 9 N.