But at even very low speeds, I cannot stop it from hitting a pier. I have not tried to do this, but every harbor master has a bunch of stories about people trying to do so and getting a leg or an arm or something squished and pulverized.
People who are not boat people rarely recognize these sorts of dangers, which is why so many get hurt on boats. "I can push us off the dock, so I can definitely keep us from hitting it." Nope, Sir Isaac Newton says you're wrong.