Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

Vffinal velocity of the object ( m/s)

Viinitial velocity of the object ( m/s)

It is important to note that Equation (10.31) is a vectoral relationship, meaning it has both

magnitude and direction. Using Equation (10.31), let us now explain why the stuntman does

not hurt himself when he jumps onto the air mat. For the sake of demonstration, let us assume

that the stuntman is jumping off a ten-story building, where the average height of each floor is

15 ft. Moreover, let us assume that he jumps onto an inflated air mat that is 15 ft tall. Neglect-

ing air resistance during his jump to make the calculation simpler, the stuntman’s velocity right

before he hits the air mat could be determined from

(10.32)

whereVirepresents the velocity of the stuntman right before he hits the air mat,gis the accel-

eration due to gravity (g32.2 ft /s

2

), andhis the height of the building minus the height of

the air mat (h135 ft). Substituting for gandhin Equation (10.32) leads to an initial veloc-

ity ofVi93.2 ft /s. Also, we realize that the air mat reduces the velocity of the stuntman to a

final velocity of zero (Vf0). Now we can solve forFaveragefrom Equation (10.31), assuming dif-

ferent values for t, and assuming a mass of 4.65 slugs (150 lbm). The results of these calcula-

tions are summarized and given in Table 10.8. It is important to note thatFaveragerepresents the

Vi 12 gh

10.7 Linear Impulse —Force Acting Over Time 291

Two stuntmen practice a fall.

Source:Kahana’s Stunt School

TABLE 10.8 The Average Reaction Force

Acting on a Stuntman

Time of Contact (s) Average Reaction Force (lbf)

0.1 4334

0.5 867

1.0 433

2.0 217

5.0 87

10.0 43

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