Two children balance on opposite ends of a seesaw. One child weighs 45 pounds and the other weighs 38 pounds. The distance between them is 10 feet. What is the distance of each child from the fulcrum (the center balance point of the seesaw)? (HINT: The product of the distance from the fulcrum and the weight of the chid must be equal on both sides of the fulcrum in order to balance the seesaw.

Question

Two children balance on opposite ends of a seesaw. One child weighs 45 pounds and the other weighs 38 pounds. The distance between them is 10 feet. What is the distance of each child from the fulcrum (the center balance point of the seesaw)? (HINT: The product of the distance from the fulcrum and the weight of the chid must be equal on both sides of the fulcrum in order to balance the seesaw.

Answer 1

The hint says it all:

45x = 38(10-x)

solve for x. Now, decide which child is "x" from the fulcrum.

Answer 2

To find the distance of each child from the fulcrum, we can use the concept of torque, which is the product of force and distance.

Let's assume that the distance of the 45-pound child from the fulcrum is x feet.

Since the two children are balancing each other, the torque on both sides of the fulcrum should be equal.

For the 45-pound child, the torque is given by multiplying their weight (45 pounds) by their distance from the fulcrum (x feet), so the torque on this side is 45x.

For the 38-pound child, the distance from the fulcrum is given as 10 - x feet (since the total distance between the children is 10 feet). Therefore, the torque on this side is 38 * (10 - x).

To balance the seesaw, the two torques must be equal, so we can set up the following equation:

45x = 38 * (10 - x)

Now, we can solve this equation to find the value of x:

45x = 380 - 38x

83x = 380

x = 380 / 83

x ≈ 4.58

Therefore, the 45-pound child is approximately 4.58 feet away from the fulcrum, and the 38-pound child is approximately 10 - 4.58 = 5.42 feet away from the fulcrum.

Answer 3

To solve this problem, we can use the concept of torque. Torque is the product of force and distance in physics. In this case, we can think of the weight of each child as the force, and the distance from the fulcrum as the distance.

Let's denote the distance of the first child from the fulcrum as x, and the distance of the second child from the fulcrum as (10 - x). So, the torque for the first child is 45 * x, and the torque for the second child is 38 * (10 - x).

To balance the seesaw, the torques on both sides of the fulcrum must be equal. Mathematically, we can represent this as an equation:

45 * x = 38 * (10 - x)

Let's solve this equation to find the value of x.

45 * x = 38 * 10 - 38 * x
45 * x + 38 * x = 38 * 10
83 * x = 380
x = 380 / 83

So, the distance of the first child from the fulcrum is approximately 4.58 feet (rounded to two decimal places).

The distance of the second child from the fulcrum can be found by subtracting the distance of the first child from the total distance between them:

10 - x = 10 - 4.58 = 5.42 feet (rounded to two decimal places).

Therefore, the first child is approximately 4.58 feet away from the fulcrum, and the second child is 5.42 feet away from the fulcrum.

The hint says it all:

Fyygdeit

To find the distance of each child from the fulcrum, we can use the concept of torque, which is the product of force and distance.

To solve this problem, we can use the concept of torque. Torque is the product of force and distance in physics. In this case, we can think of the weight of each child as the force, and the distance from the fulcrum as the distance.