In 1939 or 1940, Emanuel Zacchini took his human-cannonball act to an extreme: A
ID: 1405797 • Letter: I
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 28 m/s and at an angle of 58°. (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)?
Explanation / Answer
A)
the time taken to clear first wheel is 24/(28*cos(58))=1.61 s
height reached by that time is y = (28*sin(58)*1.61)-(0.5*9.8*1.61*1.61)
y = 25.5 m
hence clearance on the first wheel is 25.5-17 = 8.5 m
B) maximum height is Hmax = u^2*sin^2(58)/(2*g) = 28*28*sin^2(58)/(2*9.8) = 28.8 m
hence clearance on the middle wheel is 28.8-17 =11.8 m
C) Range R = u^2*sin(2*58)/g = 28*28*sin(2*58)/9.8 = 71.9 m
hence the requireddistance for C) is sqrt(71.9^2+5^2) = 72.07 m