While unrealistic, we will examine the forces on a leg when one falls from a height by approximating the leg as a uniform cylinder of bone with a diameter of 2.3 cm and ignoring any shear forces. human bone can be compressed with approximately 1.7 × 108 n/m2 before breaking. a man with a mass of 80 kgfalls from a height of 6 m. assume his acceleration once he hits the ground is constant. for these calculations, g = 10 m/s2.

what is his speed just before he hits the ground?
what is his speed just before he hits the ground?
a. 880 m/s
b. 11 m/s
c.120 m/s
d.7.7 m/s

The correct answer is b 11 m/s

Explanation:

To solve this problem we can use mechanical energy. Let's write the energy at two points: initial at the highest point and end at the lowest point

Initial

    Em₀ = U

    Em₀ = m g y.

Final

    = K

      = ½ mv2

How mechanical energy is conserved because there is no friction

    Em₀ =  

    m g y = ½ m v²

    v = √ 2 g y

Let's calculate

    v = √( 2 10 6)

    v = 11 m / s

The correct answer is b 11 m/s

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see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west