Question

A child is sitting on a swing. Its minimum and maximum heights from the ground 0.75 m and 2 m respectively, its maximum speed will be

• A. 10 m/s
• B. 5 m/s
• C. 8 m/s
• D. 15 m/s

Answer 1

The Correct Option is B

To determine the maximum speed of the swing, we can use the principles of energy conservation. When the child is at the highest point of the swing, all the energy is gravitational potential energy, and at the lowest point, it is entirely kinetic energy.

Steps to Solve:

1. Calculate the potential energy at the highest point:

   The maximum height from the ground is 2 m. The reference height, where the gravitational potential energy is zero, is at 0.75 m. Therefore, the height difference is (2 - 0.75) m = 1.25 m.

   The potential energy at the highest point U = m \cdot g \cdot h, where m is the mass of the child, g = 9.8 \, \text{m/s}^2 is acceleration due to gravity, and h = 1.25 \, \text{m}.

2. Calculate the kinetic energy at the lowest point:

   At the lowest point, the potential energy is converted into kinetic energy K = \frac{1}{2} m v^2.

3. Apply the conservation of energy principle:

   At the highest point, the potential energy is equal to the kinetic energy at the lowest point:

   m \cdot g \cdot h = \frac{1}{2} m v^2

   Cancel m from both sides (assuming mass m does not change):

   g \cdot h = \frac{1}{2} v^2

4. Solve for maximum speed v:

   v^2 = 2 \cdot g \cdot h

   v = \sqrt{2 \cdot 9.8 \cdot 1.25}

   Calculate the value:

   v = \sqrt{24.5} = 4.95 \approx 5 \, \text{m/s}

Thus, the maximum speed of the swing is approximately 5 m/s.