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
The above answer is H=21.0675
To find the height of the child at the highest point, we can make use of conservation of mechanical energy. At the highest point, the child's kinetic energy is zero, and all the energy is in the form of potential energy.
We can start by calculating the potential energy at the lowest point. The formula for gravitational potential energy is:
PE = m * g * h
Where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height. Since the mass of the child is not given in the question, we can assume it cancels out when comparing the potential energies at the highest and lowest points.
At the lowest point, the potential energy is given as:
PE_lowest = m * g * h_lowest
We can then equate this potential energy to the potential energy at the highest point, where the height is unknown:
PE_lowest = PE_highest
m * g * h_lowest = 0.5 * m * v^2
Where v is the maximum speed of the child on the swing, which is given as 4.90 m/s.
Simplifying the equation:
g * h_lowest = 0.5 * v^2
Now, we can solve for the height at the highest point:
h_highest = (0.5 * v^2) / g
Substituting the values given in the question:
h_highest = (0.5 * 4.90^2) / 9.8
Calculating:
h_highest = (0.5 * 24.01) / 9.8
h_highest = 12.005 / 9.8
h_highest ≈ 1.225 m
Therefore, the child is approximately 1.225 meters above the ground at his highest point.