The plank you are going to walk has a length of 8.76 m and a mass of 16.35 kg. The plank is not bolted down but is to be placed so that 3.17 m of the plank are actually in contact with the boat. The rest of the board overhangs the jelly fish infested waters. You have a mass of 60.3 kg. What is the minimum mass you must put on the end of the board that is still on the ship so that you can successfully walk to the end of the plank without have the board rotate you into the water

Explanation:

The center of gravity  will act at the middle point that is at 4.38 m from the end of the plank that is on boat . 16.35 x 9.8 N will act at this point .

The plank will turn around a point at 3.17 m from the end of plank that is on boat .

Suppose the weight required be W . It will be placed at the end of the plank that is on boat . The position of man is on the extreme end of the plank that is over water . So its distance from turning point will be 8.76 - 3.17 = 5.59 m .

Taking torque about turning point of all the forces like , weight of plank , weight of the person walking and force due to W

W   x 3.17 =  16.35 x ( 4.38 - 3.17 ) + 60.3 x ( 8.76 - 3.17 )

W   x 3.17 =  19.78  + 337.07 = 356.85

W = 112.57 kg .

at right angles to each other