Question

To start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 310 m/s at 50.0° above the horizontal. It explodes on the mountainside 39.0 s after firing. What are the x and y coordinates of the shell where it explodes, relative to its firing point?

Answer 1

The shell has horizontal position
`x` and vertical position
`y` at time
`t` according to

`x=\left(310(\rm m)/(\rm s)\right)\cos50.0^\circ t`

`y=\left(310(\rm m)/(\rm s)\right)\sin50.0^\circ t-\frac g2t^2`

where
`g=9.80(\rm m)/(\mathrm s^2)` is the acceleration due to gravity.

The shell explodes after 39.0 s, at which point its coordinates are

`x=7770\,\mathrm m`

`y=1810\,\mathrm m`