In 1939 or 1940, Emanuel Zacchini took his human-cannonball act to an extreme: A
ID: 1421359 • 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 25 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
horizontal component of velocity Vh using Vh = cos(58°)
initial vertical component of velocity Vv using Vv = sin(58°)
a)
If the top of the 1st wheel is a distance D1 horizontally from the firing point, the time to cover this horizontal distance is T1 = D1/Vh.
Find the height at this time using s = ut + (1/2)at^2 = Vv.T1 + (1/2)(-9.8)T1^2
Then calculate the clearance.
b)
Calculate max. height using v^2=u^2 +2as for the vertical motion giving
0^2 = Vv^2 + 2(-9.8)s where s is the max height.
Then calculate clearance.
c)
The time of flight (T) can be calculate most easily using the fact that:
initial vertical velocity component = -final vertical velocity component
v = u + at gives
-Vv = Vv + (-9.8)T
Find T then calculate the horizontal range R using
R = Vh.T
This this the required distance for the net's centre.