Suppose a child is sitting 5 feet from the fulcrum. Where does a 175 pound adult need to sit for the seesaw to be balance?

It's a levers problem.

So You need to know following.

Weight1 *Distance1(from fulcrum)=W2 *D2

What is child's weight? If 70 lb,
70 *5 =175 * X

So X=2
Adult need to sit 2 feet from the fulcrum.

To determine where the 175-pound adult needs to sit for the seesaw to be balanced, we can use the principle of moments or torque. Torque is the rotational force created by the weight acting at a distance from the fulcrum.

Let's assume that the fulcrum is in the middle of the seesaw, so each side is of equal length. Since the child is sitting 5 feet from the fulcrum, the weight of the child (let's say it's 0 pounds for now) can be represented as follows:

Torque of the child = Distance(child) × Weight(child) = 5 feet × 0 pounds = 0 lb·ft

Now, we need to find the position where the 175-pound adult should sit. Let's call it x feet. The torque created by the adult can be calculated in a similar way:

Torque of the adult = Distance(adult) × Weight(adult) = x feet × 175 pounds

To achieve balance, the torque created by the adult must be equal to the torque created by the child. So we have the equation:

Torque of the adult = Torque of the child
x feet × 175 pounds = 5 feet × 0 pounds
175x = 0

As we can see from the equation, there is no solution that satisfies the condition. Unlike a static balance, where weights can be balanced by positioning them equally on both sides of a fulcrum, a seesaw operates on the principle of torque. In this case, it is not possible to achieve a balanced position with a child and an adult of significantly different weights.

In summary, there is no specific location where the 175-pound adult can sit to balance the seesaw with a child sitting 5 feet from the fulcrum.