At the highest point of her swing, her kinetic energy is converted into potential energy, and at the lowest point, her potential energy is converted into kinetic energy. We can use the conservation of mechanical energy to find her maximum speed at the lowest point.
At the highest point:
Potential energy (PE_h) = m * g * h_h
At the lowest point:
Kinetic energy (KE_l) = 0.5 * m * v^2
Potential energy (PE_l) = m * g * h_l
Conservation of mechanical energy:
PE_h = KE_l + PE_l
Since we only need to find her maximum speed, we don't need to worry about the mass (m) as it will cancel out.
Substituting the values:
(9.8 m/s²)(4.1 m) = 0.5(v^2) + (9.8 m/s²)(0.8 m)
Solving for v:
(9.8)(4.1-0.8) = 0.5(v^2)
9.8 * 3.3 = 0.5(v^2)
v^2 = (9.8 * 3.3) / 0.5
v^2 = 64.34
v = √64.34
v ≈ 8.02 m/s
The girl's maximum speed is approximately 8.02 m/s.
A girl swings on a playground swing in such a way that at her highest point she is 4.1 m from the ground, while at her lowest point she is 0.8 m from the ground.What is her maximum speed? The acceleration due to gravity is 9.8 m/s2 .Answer in units of m/s.
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