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=(v^2_o\sin(2\theta))/(g) \\ t=(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=(v^2_o\sin(2\theta))/(g)=(v^2_o\sin(2\cdot40))/(g)=0.98(v^2_o)/(g) \\ t_1=(2v_o\sin\theta)/(g)=(2v_o\sin(40))/(g)=0.64\frac{v^{}_o}{g} \end{gathered}`

second projectile:

`\begin{gathered} R_1=(v^2_o\sin(2\theta))/(g)=(v^2_o\sin (2\cdot50))/(g)=0.98(v^2_o)/(g) \\ t_1=(2v_o\sin\theta)/(g)=(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