A projectile is thrown with velocity U = 20 | vedclass

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(A) The formula for the range $R$ of a projectile is $R = \frac{U^2 \sin(2	heta)}{g}$.Given $U = 20 \ m/s$,$	heta = 60^{\circ}$,and $g \approx 10 \

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$39.0$

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(A) The formula for the range $R$ of a projectile is $R = \frac{U^2 \sin(2	heta)}{g}$.Given $U = 20 \ m/s$,$	heta = 60^{\circ}$,and $g \approx 10 \ m/s^2$.$R = \frac{20^2 	imes \sin(120^{\circ})}{10} = \frac{400 	imes \frac{\sqrt{3}}{2}}{10} = 20\sqrt{3} \approx 34.64 \ m$.The relative error in $U$ is $\frac{\Delta U}{U} = 5\% = 0.05$.Since $R \propto U^2$,the relative error in range is $\frac{\Delta R}{R} = 2 	imes \frac{\Delta U}{U} = 2 	imes 0.05 = 0.10$.Thus,$\Delta R = 0.10 	imes R = 0.10 	imes 34.64 = 3.464 \ m$.The possible range lies in the interval $(R - \Delta R, R + \Delta R) = (34.64 - 3.46, 34.64 + 3.46) = (31.18 \ m, 38.10 \ m)$.Comparing the options,$39.0 \ m$ lies outside this range.

$A$ projectile is thrown with velocity $U = 20 \ m/s \pm 5\%$ at an angle $60^{\circ}.$ If the projectile falls back on the ground at the same level,then which of the following values in $m$ cannot be a possible answer for the range?

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