A child of mass 40.0 kg is swinging on a swing with ropes of length 4.0 m. How long does it take the child to swing from the maximum height on one side to the other?

Half of the period of the swing (which is essentially a pendulum).

It will be independent of the mass.

The period of a pendulum is
2 pi sqrt(L/g)
Half of that will be your answer.
Having two ropes instead of one does not change the formula from that of a simple pendulum.

Thanks. I was confused by the way the question was worded and my answer was 2 times bigger than what the answer is supposed to be.

To find the time it takes for the child to swing from the maximum height on one side to the other, we can use the pendulum formula:

T = 2π√(L/g)

Where:
T = Time period
π = Pi, approximately 3.14
L = Length of the pendulum (ropes in this case)
g = Acceleration due to gravity (approximately 9.8 m/s²)

Let's substitute the given values into the formula and calculate:

T = 2π√(4.0 m / 9.8 m/s²)

First, divide the length of the pendulum (4.0 m) by the acceleration due to gravity (9.8 m/s²):

T = 2π√0.4082

Next, calculate the square root of 0.4082:

T = 2π * 0.6388

Multiply 2π by 0.6388:

T ≈ 4.02 seconds

Therefore, it takes approximately 4.02 seconds for the child to swing from the maximum height on one side to the other.

To find the time it takes for the child to swing from one side to the other, we can use the principles of simple harmonic motion.

The time period of a pendulum (or swing) can be calculated using the formula:

T = 2π√(L/g)

Where:
T is the time period (the time it takes for one complete swing)
π is a mathematical constant approximately equal to 3.14159
L is the length of the swing's ropes
g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)

In this case, the length of the swing's ropes (L) is given as 4.0 m. Therefore, we can substitute these values into the formula to find the time period:

T = 2π√(4.0/9.8)
= 2π√(0.4082)
≈ 2π(0.6398)
≈ 4.009 seconds

So, it would take the child approximately 4.009 seconds to swing from the maximum height on one side to the other.