Answer:
h = 2.15 m
Explanation:
Given that,
Mass of the child, m = 35 kg
The child reaches the bottom at a speed of 6.5 m/s
We need to find the height slide by a frictionless playground slide. Let it is equal to h. Using the conservation of energy to find it as follows :
[tex]\dfrac{1}{2}mv^2=mgh\\\\h=\dfrac{v^2}{2g}\\\\h=\dfrac{(6.5)^2}{2\times 9.8}\\\\h=2.15\ m[/tex]
So, it will slide to a height of 2.15 m
The height slid by the frictionless playground can be calculated by equating the kinetic and potential energy equations which is 2.16 meters
K.E = P.E
K. E = 0.5mv² ; P.E = mgh
0.5mv² = mgh
gh = 0.5v²
h = [(0.5v²) ÷ g]
h = [(0.5 × 6.5²) ÷ 9.8]
h = (21.125 ÷ 9.8)
h = 2.155 m
Therefore, the height slid by a frictionless playground is 2.16 meters
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