Chapter 9, Problem 7P

An estimate of the minimum velocity required for a round flat stone to skip when it hits the water is given by (Lyderic Bocquet, “The Physics of Stone Skipping,” Am. J. Phys., vol. 71, no. 2, February 2003):

$V=\frac{\sqrt{\frac{16Mg}{\pi C{\rho }_w{d}^2}}}{\sqrt{1-\frac{8M{\tan }^2\beta }{\pi d^{3}C{\rho }_w\sin \theta }}}$

where M and d are the stone mass and diameter, ρ_w, is the water density, C is a coefficient, θ is the tilt angle of the stone, is the incidence angle, and

g = 9.81 m/s². Determine d if V = 0.8 m/s. (Assume that M = 0.1 kg,

C = 1, ρ_w=l,000kg/m³, and ß= θ= 10°.)