Answer to Question #262414 in Physics for Leyaa

Question #262414

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?


1
Expert's answer
2021-11-07T19:25:20-0500

a) We have range and max. height:


R=v2sin(2θ)g=v22sinθcosθg, y=v2sin2θ2g=v2sinθsinθ2g, yR=14tanθ, θ=arctan4yR=arctan4(182.5)10.63=80°. v=Rgsin(2θ)=17.5 m/s.R=\frac{v^2\sin(2\theta)}{g}=\frac{v^2·2\sin\theta·\cos\theta}{g},\\\space\\ y=\frac{v^2\sin^2\theta}{2g}=\frac{v^2·\sin\theta·\sin\theta}{2g},\\\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) He fell from the max. height of (18) m to the ground:



uy=2gH=18.8 m/s,ux=vx=vcosθ=3.04 m/s,u=ux2+uy2=19 m/s.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}.


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