# A young child is swinging at the playground. At the lowest part of the swing, the velocity of the swing and student is 7.5 m/s. The swing and the child together have a mass of 25 kg. How many meters high did the child swing?

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A young child is swinging at the playground. At the lowest part of the swing, the velocity of the swing and student is 7.5 m/s. The swing and the child together have a mass of 25 kg. How many meters high did the child swing?

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Step 1

The motion of a child swinging on a swing is similar to the motion of a simple pendulum which can be identified as a simple harmonic motion. The lowest part of the swing corresponds to the equilibrium point of the system. The conservation of mechanical energy can be applied to this system to find the height by which the child swings.

Step 2

The child starts swinging from an initial position at a particular height. At that point, the system (child + swing) has only gravitational potential energy since initially the system is at rest. When the system moves and reaches the equilibrium point, all its potential energy is converted to kinetic energy. In the forward motion from the equilibrium position, the speed of the system decreases and hence the kinetic energy reduces and the system acquires potential energy, and the entire kinetic energy it had get converted to potential energy again at the highest point. This happens due to the conservation of mechanical energy in the system. The expression for the kinetic energy and potential energy of the system is given in equation (1) and (2) respectively.

Step 3

Since the kinetic energy the system had at the equilibrium position (the lowest point of the swing) is ...

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### Kinematics 