What height does a frictionless playground slide need so that a 35 kg child reaches the bottom at a speed of 6.5 m/s?

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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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 :

So, it will slide to a height of 2.15 m

f=ma newton's second law 7x8=56n