Question

Emmanuel Zacchini launched as a human cannonball in 1940 soared over three Ferris wheels each 18.0 m high covering a horizontal distance of 10.63m. a.) Assuming that the point of projection is 2.50 m above the ground and that he landed safely on a net placed at the same level, find his initial velocity. b.) Assuming that he missed the net and landed on the ground, with what velocity will he strike the ground?

Answer 1

a) For the given values of max. height and range write corresponding equations and then divide height by range:

$$y=\frac{v^2\sin^2\theta}{2g}=\frac{v^2·\sin\theta·\sin\theta}{2g},\\\space\\ R=\frac{v^2\sin(2\theta)}{g}=\frac{v^2·2\sin\theta·\cos\theta}{g},\\\space\\ \frac yR=\frac14\tan\theta,\\\space\\ \theta=\arctan\frac{4y}{R}=\arctan\frac{4(18-2.5)}{10.63}=80°.\\\space\\ v=\sqrt\frac{Rg}{\sin(2\theta)}=17.5\text{ m/s}.$$

b) Considering that Emmanuel Zacchini had additional 2.5 m:

$$u_y=\sqrt{2gH}=18.8\text{ m/s},\\ u_x=v_x=v\cos\theta=3.04\text{ m/s},\\ u=\sqrt{u_x^2+u_y^2}=19\text{ m/s}.$$