Answer to Question #160625 in Mechanics | Relativity for Lenovo

Question

To start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 300m/s at 55oC above the horizontal.It explodes on the mountainside after 42.0s after firing. What are the x an y coordinates of the shell where it explodes, relative to its firing point?

Answer 1

The $x$-coordinate of the shell can be found as follows:

$$x=v_0tcos\theta,$$ $$x=300\ \dfrac{m}{s}\cdot42\ s\cdot cos55^{\circ}=7227\ m.$$

The $y$-coordinate of the shell can be found as follows:

$$y=v_0tsin\theta-\dfrac{1}{2}gt^2,$$ $$y=300\ \dfrac{m}{s}\cdot42\ s\cdot sin55^{\circ}-\dfrac{1}{2}\cdot9.8\ \dfrac{m}{s^2}\cdot(42\ s)^2=1678\ m.$$