Your question touches upon an important concept in physics known as the principle of relativity. The principle of relativity, in its simplest form, states that the laws of physics should be the same for all observers, regardless of their relative motion. This principle was first introduced by Galileo and later developed further by Albert Einstein in his theory of special relativity.
According to the theory of special relativity, the speed of light in a vacuum is constant and is the same for all observers, regardless of their relative motion. This constant speed of light, denoted by 'c,' is approximately 299,792 kilometers per second.
In your example, if you are moving at a velocity of 10 feet per second north and shine a laser beam northwards, according to the principle of relativity, the measured speed of light would still be 'c' for all observers, regardless of their motion. This means that even though you are moving, you would measure the speed of light to be the same value of 'c,' not 10 feet per second + 'c.'
The Michelson-Morley experiment you mentioned was conducted in the late 19th century to detect the motion of the Earth through a hypothetical medium called the luminiferous ether, which was thought to be the medium through which light waves propagated. However, the experiment did not detect any significant change in the measured speed of light due to the Earth's motion. This result was unexpected and led to the development of special relativity, which explains the constancy of the speed of light.
In summary, according to the principle of relativity and our understanding of special relativity, the speed of light is always measured to be the same value 'c' for all observers, regardless of their motion relative to the source of light. This concept has been extensively tested and confirmed by numerous experiments and observations.