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)

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
and at an angle of
. (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)?

The Correct Answer and Explanation is:

To analyze Emanuel Zacchini’s human-cannonball trajectory, the problem can be treated as a projectile motion scenario. Given his initial speed of 26.5 m/s and launch angle of 53.0°, the trajectory equations can be used to determine the clearances and the landing position.

(a) Clearance over the first Ferris wheel

The horizontal distance to the first wheel is 28 m, and its height is 18 m. The vertical position of Zacchini at this distance is determined using the projectile motion equation:

y=xtan⁡θ−gx22v02cos⁡2θy = x \tan \theta – \frac{g x^2}{2 v_0^2 \cos^2\theta}

where gg is gravitational acceleration (9.81 m/s²), x=28x = 28 m, θ=53.0∘\theta = 53.0^\circ, and v0=26.5v_0 = 26.5 m/s.

After calculating, his height at this position is approximately 24.5 m, meaning he clears the first wheel by 6.5 m.

(b) Clearance over the middle wheel

Maximum height occurs when vertical velocity becomes zero, given by:

hmax⁡=v02sin⁡2θ2gh_{\max} = \frac{v_0^2 \sin^2\theta}{2g}

Substituting the values, the maximum height achieved is 28.1 m. Since the middle Ferris wheel is 18 m high, he clears it by 10.1 m.

(c) Position of the net

The range of his flight is determined by:

R=v02sin⁡2θgR = \frac{v_0^2 \sin 2\theta}{g}

Using the given values, the landing position is 63.5 m from the cannon.

Explanation

Zacchini’s launch followed the principles of projectile motion, where the trajectory depended on both horizontal and vertical motion components. The highest clearance was achieved over the middle wheel, as vertical velocity became zero before descending. The net placement required estimating the horizontal range, using the standard equation for projectile motion in the absence of air resistance. This example highlights how physics governs even dramatic stunts like a human cannonball performance.