What do scientists use a scientific law for?

Why does the input force have to be greater than the force needed to lift the bale?

Aproton is projected toward a fixed nucleus of charge +ze with velocity vo. initially the two particles are very far apart. when the proton is a distance r from the nucleus its velocity has decreased to 1/2vo. how far from the nucleus will the proton be when its velocity has dropped to 1/4vo?

Jasmine is diving off a 3-meter springboard. her height in meters above the water when she is x meters horizontally from the end of the board is approximated by the equation h=-x^2+3x+3. what is the maximum height jasmine will reach on her dive?