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Sagot :
In order to determine which of the given sentence is true, take into account the following formulas for the range and total time of the trajectory of a body, in a parabolic motion.
[tex]\begin{gathered} R=\frac{v^2_o\sin(2\theta)}{g} \\ t=\frac{2v_o\sin\theta}{g} \end{gathered}[/tex]replace the values of the given angles for both projectiles and compare the results, as follow:
first projectile:
[tex]\begin{gathered} R_1=\frac{v^2_o\sin(2\theta)}{g}=\frac{v^2_o\sin(2\cdot40)}{g}=0.98\frac{v^2_o}{g} \\ t_1=\frac{2v_o\sin\theta}{g}=\frac{2v_o\sin(40)}{g}=0.64\frac{v^{}_o}{g} \end{gathered}[/tex]second projectile:
[tex]\begin{gathered} R_1=\frac{v^2_o\sin(2\theta)}{g}=\frac{v^2_o\sin (2\cdot50)}{g}=0.98\frac{v^2_o}{g} \\ t_1=\frac{2v_o\sin\theta}{g}=\frac{2v_o\sin (50)}{g}=0.76\frac{v^{}_o}{g} \end{gathered}[/tex]Then, based on the previous results, youcan notice that both obtain the same range but the first projectile hits the ground with a lower time. None of the given options describes the previous result, then, you have:
D) None of the above
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