Two children are playing on the seesaw. THe lighter child is 9 feet from the fulcrum, and the heavier child is 6 feet from the fulcrum. As the lighter child goes from the ground to the highest point, she travels through an angle of 35 degrees in 1/2 second.

a. find the angular velocity of each child.

b. What is the linear velocity of each child?

Since you are so adamant on an answer, I will attempt this. I'm not 100% sure, though.

a. angular velocity = angle traversed / time
a = 35 / .5 = 70 degrees per second

b. Multiply angular velocity by radius.
70 * ((9+6)/2)
70 * 7.5
525 ft/sec

Be warned... I'm not sure about those answers.

Actually, I believe they want a different answer for each child. I didn't account for that, so I have no idea.

To find the angular velocity of each child, we can use the formula:

Angular velocity = angle / time

a) For the lighter child:
Angle = 35 degrees
Time = 1/2 second

Angular velocity (lighter child) = 35 degrees / (1/2 second)
Angular velocity (lighter child) = 35 degrees / 0.5 second
Angular velocity (lighter child) = 70 degrees per second

b) To find the linear velocity of each child, we can use the formula:

Linear velocity = angular velocity * radius

For the lighter child:
Angular velocity (lighter child) = 70 degrees per second
Radius (lighter child) = 9 feet

Linear velocity (lighter child) = 70 degrees per second * 9 feet
Linear velocity (lighter child) = 630 feet per second

For the heavier child:
Angular velocity (heavier child) = 70 degrees per second
Radius (heavier child) = 6 feet

Linear velocity (heavier child) = 70 degrees per second * 6 feet
Linear velocity (heavier child) = 420 feet per second

To find the angular velocity of each child, we need to use the formula:

Angular velocity (ω) = θ / t

where θ is the angle traveled and t is the time taken.

a. For the lighter child:
Since the lighter child travels through an angle of 35 degrees in 1/2 second, we can plug in these values into the formula:

Angular velocity (ω) = 35 degrees / 0.5 seconds
= 70 degrees per second

So, the angular velocity of the lighter child is 70 degrees/second.

For the heavier child:
Since the heavier child is not given any information about the angle traveled or time taken, we cannot directly calculate the angular velocity. We need more information such as the time taken or the angle traveled.

b. The linear velocity can be calculated using the formula:

Linear velocity (v) = r * ω

where r is the distance from the fulcrum and ω is the angular velocity.

For the lighter child:
The distance of the lighter child from the fulcrum is given as 9 feet. We know the angular velocity is 70 degrees/second.

Linear velocity (v) = 9 feet * (70 degrees/second)
= 630 feet per second

So, the linear velocity of the lighter child is 630 feet/second.

For the heavier child:
We need more information, such as the angular velocity, to calculate the linear velocity. Since the angular velocity of the heavier child is not given, we cannot find its linear velocity with the given information.