A mother and daughter are on a seesaw in the
park.
How far from the center must the 127 lb
mother sit in order to balance the 49 lb daughter sitting 7 ft from the center?
127*distance=49*7
solve for distance
To determine the distance from the center at which the 127 lb mother must sit to balance the 49 lb daughter, we can use the principle of moments. The principle of moments states that the sum of the clockwise moments is equal to the sum of the counterclockwise moments.
In this case, the counterclockwise moment is caused by the daughter, and the clockwise moment is caused by the mother. The moment is defined as the product of the weight of an object and its distance from the fulcrum (in this case, the center).
Let's denote the distance the mother needs to sit from the center as x. The daughter is already sitting 7 ft from the center, so her moment is 49 lb * 7 ft = 343 lb-ft. The mother's moment is 127 lb * x ft = 127x lb-ft.
Since the sum of the moments is zero for the seesaw to be balanced, we have the equation:
343 lb-ft + 127x lb-ft = 0
Simplifying the equation, we get:
127x lb-ft = -343 lb-ft
Dividing both sides by 127 lb-ft, we find:
x = -343 lb-ft / 127 lb-ft
x ≈ -2.70 ft
The negative sign indicates that the mother needs to sit to the left of the center, which makes sense since she is heavier than the daughter. Therefore, the mother must sit approximately 2.70 ft to the left (towards the center) of the center in order to balance the seesaw with the 49 lb daughter sitting 7 ft from the center.