Final answer:
To find the girl's speed at 60cm on a swing, you can apply the conservation of mechanical energy. Potential energy at the highest point is converted to kinetic energy at the lowest, allowing you to calculate the speed with the difference in height and the acceleration due to gravity. The speed of the girl is 4.84m/s.
Step-by-step explanation:
The question you've asked is about calculating the speed of a girl on a swing at a lower height given the information that her speed is zero when she is at the highest point, 180cm above the ground. This scenario is an excellent example of the conservation of mechanical energy in physics, assuming there is no air resistance or other non-conservative forces at work.
When the girl is at 180cm, all of her mechanical energy is in the form of potential energy since her speed (and thus her kinetic energy) is zero. As she swings down to 60cm, her potential energy is converted into kinetic energy. The conservation of energy principle dictates that the total mechanical energy is constant if only conservative forces are doing work. This can be mathematically described by the equation:
Potential Energy at 180cm = Kinetic Energy at 60cm
Using the formula for potential energy (PE = mgh) and kinetic energy (KE = 1/2 mv2), and setting these equal since the mechanical energy is conserved, you can solve for the girl's speed at 60cm:
mgh = 1/2 mv2 (mass is the same and cancels out)
gh = 1/2 v2
Solving for v gives us:
v = sqrt(2gh)
By substituting h with the difference in height (1.8m - 0.6m), and g with the acceleration due to gravity (approximately 9.8 m/s2), you can find the girl's speed at 60cm.
v = sqrt(2gh)
= sqrt(2*9.8*1.2)
=4.84m/s