In 1939 or 1940, Emanuel Zacchini took his human-cannonball act to an extreme: A

Question

In 1939 or 1940, Emanuel Zacchini took his human-cannonball act to an extreme: After being shot from a cannon, he soared over three Ferris wheels and into a net (see the figure). Assume that he is launched with a speed of 27 m/s and at an angle of 59. (a) Treating him as a particle, calculate his clearance over the first wheel. (b) If he reached maximum height over the middle wheel, by how much did he clear it? (c) How far from the cannon should the net's center have been positioned (neglect air drag)? = 27% 5.0m Ner 0m ,-59 26m (a) Numbern126.14 (b) Number 127.3276 (c) Number 5.68 (b) Number 127.527 Units m

Explanation / Answer

a)

Horizontal Velocity

Vy=VoCos59 =27Cos59 =13.91 m/s

Vertical Velocity

Vx=VoSin59 =27Sin59 =23.14 m/s

Time Taken to clear the first wheel is

t=X/Vx=26/13.91=1.87 s

So Vertical Distance reached is

Y=Vyt+(1/2)at2 =23.14*1.87+(1/2)(-9.8)*1.872

Y=26.13 m

Since he begains 5 m of the ground he clears the first wheel by

d=(26.13+5)-18=13.13 m

b)

Maximum Height reached is

hmax=V2Sin(o)/2g =272Sin59/2*9.8

hmax=31.88 m

Since he begains 5 m of the ground he clears the middle wheel by

d=(31.88+5)-18 =18.88 m

c)

Range

R=V2sin2(o)/g =272*sin59/9.8

R=65.68 m

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