Question

How high would the board need to be for a 175 pound man to reach terminal velocity by the time he hit the water?

We were not giving the terminal velocity. That was the only information we recieve along with a link https://www.wikihow.com/Calculate-Terminal-Velocity.

Answer 1

Solution:

Let us go to the basics first.

We shall take some rough values of the variables required to make our calculation simpler and easier so that we enable ourselves to calculate the terminal velocity. Our answer may vary depending upon this.

We know that, the terminal velocity, v is given by following relation:

v = √[(2mg) / (ρAC)]

[where, m = 175 pound = 79.38 kg; g = acceleration due to gravity = 9.8 m/s²; ρ = the density of air at sea level when the temperature is 15 °C is 1.225 kg/m³; A = projected area of the object or man = Area projected by the foot of man = 1 ft² (assumed) = 0.093 m²; C = coefficient of drag for a person falling upright = 1]

Thus, v = √[(2*79.38*9.8) / (1.225*0.093*1)] = 116.86 m/s (Approximated Terminal velocity)

Now, we also know that for a person falling under gravity,

v = √[2gh]

=> v² = 2gh

=> h = v²/2g

=> h = (116.86)² / (2*9.8) = 696.74 m or 2285.9 ft (Approximated height of board) (Answer)