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(B) When a ball strikes a surface,the component of velocity parallel to the surface remains unchanged (assuming no friction),while the component perpe

Vedclass · Accepted Answer

$60$

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(B) When a ball strikes a surface,the component of velocity parallel to the surface remains unchanged (assuming no friction),while the component perpendicular to the surface changes according to the coefficient of restitution $e$.$1$. The horizontal component of velocity remains constant:$v' \sin 	heta = v \sin 45^{\circ}$  --- $(1)$$2$. The vertical component of velocity after impact is given by $v'_{y} = e v_{y}$:$v' \cos 	heta = e (v \cos 45^{\circ})$  --- $(2)$$3$. Dividing equation $(1)$ by equation $(2)$:$\frac{v' \sin 	heta}{v' \cos 	heta} = \frac{v \sin 45^{\circ}}{e v \cos 45^{\circ}}$$	an 	heta = \frac{	an 45^{\circ}}{e}$$4$. Given $e = 1/\sqrt{3}$ and $	an 45^{\circ} = 1$:$	an 	heta = \frac{1}{1/\sqrt{3}} = \sqrt{3}$$5$. Therefore,$	heta = 	an^{-1}(\sqrt{3}) = 60^{\circ}$.

$A$ ball strikes a horizontal surface as shown in the figure. If the coefficient of restitution is $e = 1/\sqrt{3}$,then the angle $\theta$ is ............... $^o$.

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