The world's fastest humans can reach speeds of about 11 m/s. In order to increase his gravitational potential energy by an amount equal to his kinetic energy at full speed, how high would such a sprinter need to climb?

Question

Physics

Roy Harris

16 June, 17:21

The world's fastest humans can reach speeds of about 11 m/s. In order to increase his gravitational potential energy by an amount equal to his kinetic energy at full speed, how high would such a sprinter need to climb?

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Answers (1)

Know the Answer?

Hayden Freeman · Answer 1

The sprinter need to climb 6.17 m

Explanation:

From the question,

Ep = Ek ... Equation 1

Where Ep = potential energy, Ek = kinetic energy.

therefore,

mgh = 1/2mv² ... Equation 2

Where m = mass of the human, v = speed, h = height, g = acceleration due to gravity.

making h the subject of formula in equation 2

h = 1/2v²/g ... Equation 3

Given: v = 11 m/s

Constant: g = 9.8 m/s²

Substituting these values into equation 3,

h = 1/2 (11²) / 9.8

h = 6.17 m.

Therefore the sprinter need to climb 6.17 m