Question

Two projectiles are fired at equal speeds but different angles. One is fired at an angle of 40° and the other at 50°. With no air resistance,A) The one with 40° will hit the ground first but with a lower range.B) The one with 50° will hit the ground later but with a lower range.C) both hit at the same time and with the same range.D) None of the above

Answer 1

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.

$\begin{gathered} R=\frac{v^2_o\sin(2\theta)}{g} \\ t=\frac{2v_o\sin\theta}{g} \end{gathered}$

replace the values of the given angles for both projectiles and compare the results, as follow:

first projectile:

$\begin{gathered} R_1=\frac{v^2_o\sin(2\theta)}{g}=\frac{v^2_o\sin(2\cdot40)}{g}=0.98\frac{v^2_o}{g} \\ t_1=\frac{2v_o\sin\theta}{g}=\frac{2v_o\sin(40)}{g}=0.64\frac{v^{}_o}{g} \end{gathered}$

second projectile:

$\begin{gathered} R_1=\frac{v^2_o\sin(2\theta)}{g}=\frac{v^2_o\sin (2\cdot50)}{g}=0.98\frac{v^2_o}{g} \\ t_1=\frac{2v_o\sin\theta}{g}=\frac{2v_o\sin (50)}{g}=0.76\frac{v^{}_o}{g} \end{gathered}$

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