two small kids weighing 10kg and 15kg are trying to balance on a seesaw of total length 5 m with the fulcrum at the centre. if one of the kids is sitting at an end where should the other sit?

To balance the seesaw, the total torque on both sides of the fulcrum should be equal. Torque is calculated by multiplying the weight of an object by its distance from the fulcrum.

Let's denote the distance between the fulcrum and the first kid (10 kg) as x, and the distance between the fulcrum and the second kid (15 kg) as y. Since the total length of the seesaw is 5 m, we have the following relationship:

x + y = 5 m

The torque on the left side (where the first kid is sitting) is 10 kg * x, and the torque on the right side (where the second kid is sitting) is 15 kg * y. Since the seesaw is balanced, the torques must be equal:

10 kg * x = 15 kg * y

Now we have a system of two equations:

x + y = 5
10x = 15y

We can solve this system of equations to find the values of x and y.

From the second equation, we can isolate y:

y = (10/15) * x
y = (2/3) * x

Substituting this value of y into the first equation, we have:

x + (2/3) * x = 5
(5/3) * x = 5
x = 5 * (3/5)
x = 3 m

Therefore, the first kid should sit at a distance of 3 meters from the fulcrum, and the second kid should sit at a distance of 2 meters from the fulcrum.

To determine where the second kid should sit on the seesaw, we need to consider the weight and distance from the fulcrum for both children.

Let's denote the distance from the fulcrum to the heavier child as "x" and the distance from the fulcrum to the lighter child as "y". Since the fulcrum is at the center of the seesaw, the total length of the seesaw is 5 meters, so x + y = 5.

We also know the weights of the children: 10kg and 15kg. To maintain balance, the torque on each side of the fulcrum should be equal. The torque can be calculated by multiplying the weight by the distance from the fulcrum:

Torque1 = weight1 * distance1
Torque2 = weight2 * distance2

In this case, since the fulcrum is at the center, distance1 = x and distance2 = y.

To balance the seesaw, we need to ensure that Torque1 = Torque2. Given the weights, we have:

10kg * x = 15kg * y

Now we can solve the equations simultaneously:

x + y = 5 --(1)
10x = 15y --(2)

We will solve this system of equations to find the values of x and y.

From equation (1), we can isolate x:
x = 5 - y

Substituting this value in equation (2):
10(5 - y) = 15y
50 - 10y = 15y
50 = 25y
y = 2

Now that we have the value of y, we can find x:
x = 5 - y
x = 5 - 2
x = 3

So, the child weighing 10kg should sit 3 meters from the fulcrum, and the child weighing 15kg should sit 2 meters from the fulcrum to balance the seesaw.

W1*d1 = W2*d2.

10 * 2.5 = 15*d2.
d2 = 25/15 = 1.67 m. from the center.
d2 = 2.5-1.67 = 0.83 m. from the end.