A person jumps from the roof of a house 3.5-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.71 m .


If the mass of his torso (excluding legs) is 45 kg , find the magnitude of the average force exerted on his torso by his legs during deceleration.

Answer :

The force exerted on his torso by his legs during the deceleration is 4365 N.

Explanation:

Mass of the torso m=45kg

Height of the building s=3.5 m

Decelerating distance=0.71 m

when he jumps to the ground, the only acceleration is acceleration due to gravity g

motion1 from top to ground

initial velocity u=0

we have to calculate final velocity v using the following equation of motion.

[tex]v^2-u^2=2gs\\v^2-0^2=2\times 9.8\times3.5=68.6\\v=\sqrt{68.6} \\=8.3[/tex]

use height of the building as the distance s as the jump from top to the ground is only described here.

Motion 2 on the ground

v=0

u=8.3(final  velocity of motion 1)

The deceleration after striking the ground can  be calculated from the equation of motion

[tex]v^2-u^2=2as\\\\a=v^2-u^2/2\times 0.71\\=0^2-8.3^2/0.71=97 m/s^2[/tex]

The decelerating distance is used in the place of s since since the motion after hitting the ground is described in this case.

The equation of force is

[tex]F=ma\\=45\times 97=4365 N[/tex]

The magnitude of the average force exerted on his torso by his legs during deceleration is 2,172.6 N.

The given parameters;

  • height of the house, h = 3.5 m
  • distance of deceleration, d = 0.71 m
  • mass of the tensor, m = 45 kg;

The final speed of the person when he jumps to ground is calculated as;

[tex]\frac{1}{2} mv^2 = mgh\\\\v^2 = 2gh\\\\v = \sqrt{2gh} \\\\v = \sqrt{2\times 9.8 \times 3.5 } \\\\v = 8.28 \ m/s[/tex]

The deceleration of the torso over the given distance is calculated as;

[tex]v^2 = u^2 + 2as\\\\a = \frac{v^2 - u^2}{2s} \\\\a = \frac{0-8.28^2}{2\times 0.71} \\\\a = -48.28 \ m/s^2[/tex]

The magnitude of the average force exerted on his torso by his legs during deceleration is calculated as;

[tex]F = ma\\\\F = 45 \times 48.28\\\\F = 2,172.6 \ N[/tex]

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