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 48°. (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)? 4.0m 18m 4.0mNet = 480 24m

Explanation / Answer

here,

initial speed , u = 27 m/s

theta = 48 degree

a)

the height at x = 24 m

y1 = x * tan(theta) - g * x^2 /( 2 * u^2 * cos^2(theta))

y1 = 24 * tan(48) - 9.81 * 24^2 /( 2 * 27^2 * cos^2(48))

y1 = 18 m

the clearance above the wheel = y1 - 18 = 0 m

b)

the maximum height , y2 = (u * sin(theta))^2 /( 2 * g)

y2 = ( 27 * sin(48))^2 /( 2 * 9.8) m

y2 = 20.5 m

the clearance above the wheel = 20.5 - 18 = 2.54 m

c)

the distance of net center , R = u^2 * sin(2 * theta) /g

R = 74 m

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