The maximum speed of a child on a swing is 4.90 m/s. The child's height above the ground is 0.525 m at the lowest point in his motion. How high above the ground is he at his highest point?

h₀=0.525 m, v = 4.9 m/s, H=?

mv²/2= mgh
h= v²/2g
H=h+h₀= v₀²/2g + h₀

To determine the height of the child at his highest point on the swing, we can use the principle of conservation of mechanical energy.

The energy of the child on a swing is a combination of gravitational potential energy and kinetic energy.

At the highest point of the swing, the child's kinetic energy is zero because the child momentarily comes to rest. Therefore, all the initial energy is in the form of gravitational potential energy.

The formula for gravitational potential energy is given by:

PE = m * g * h

Where PE is the gravitational potential energy, m is the mass of the child, g is the acceleration due to gravity, and h is the height.

Since the mass of the child is not provided and is not essential to solving this problem, we can disregard it. The acceleration due to gravity, g, is approximately 9.8 m/s².

Given that the child's height at the lowest point is 0.525 m and all the energy is in the form of gravitational potential energy, we can set up the following equation:

PE_lowest = PE_highest

m * g * h_lowest = m * g * h_highest

Since the mass cancels out, we can simplify the equation to:

h_highest = h_lowest

Therefore, the child's height at the highest point is also 0.525 m.