Question

kelli has a mass of 42 kg, and she is sitting on a playground swing that hangs 4 m above the ground. she pulls the swing back and releases it when the seat is 1 meter above the ground. her mom the swing passes through its lowest point? how fast is kelli moving when

Explanation:

Step1: Determine the height difference

The initial height of the swing seat is 1 m above the ground, and at the lowest point, it's 0.4 m above the ground. So the height difference $\Delta h = 1 - 0.4 = 0.6$ m.

Step2: Apply conservation of mechanical energy

Assuming no air resistance, the gravitational potential energy at the highest point is converted into kinetic energy at the lowest point. The formula for gravitational potential energy is $U = mgh$ and kinetic energy is $K = \frac{1}{2}mv^2$. Setting $U = K$:
$$mgh = \frac{1}{2}mv^2$$
We can cancel out the mass $m$ from both sides:
$$gh = \frac{1}{2}v^2$$

Step3: Solve for velocity $v$

We know $g = 9.8 \, \text{m/s}^2$ and $h = 0.6 \, \text{m}$. Rearranging the formula:
$$v = \sqrt{2gh}$$
Substitute the values:
$$v = \sqrt{2 \times 9.8 \times 0.6}$$
$$v = \sqrt{11.76}$$
$$v \approx 3.43 \, \text{m/s}$$

Answer:

Kelli is moving at approximately $\boldsymbol{3.43 \, \text{m/s}}$ when the swing passes through its lowest point.