Answer :
To balance the board with a 67kg adult and a 30kg child on opposite ends, the pivot should be placed approximately 6.41m from the child's end. This is found using the principle of moments, where both sides of the seesaw must have equal moments to be in equilibrium.
To find the correct position for the pivot to balance the board with a 67kg adult at one end and a 30kg child on the other end, we can use the principle of moments. The moment is the product of the force applied and the distance from the pivot point where the force is applied. For the seesaw to be balanced, the moments on both sides of the seesaw must be equal.
To calculate the distance 'x' from the pivot to the child (30kg), we can set the moments around the pivot point equal to each other. The equation will be the weight of the adult (67kg) times his distance from the pivot (let's assume this distance to be '9.3 - x' since the board's total length is 9.3m) equal to the weight of the child (30kg) times the child's distance from the pivot (which is 'x'). This is mathematically represented as:
67kg * (9.3m - x) = 30kg * x
Solving for 'x' gives us:
x = (67kg * 9.3m) / (67kg + 30kg)
x = 622.1kg*m / 97kg
x \u2248 6.41m
So, the pivot should be placed approximately 6.41m from the end where the child sits to balance the board.
