How far from the castle wall does the launched rock hit the ground?

King Arthur's knights use a catapult to launch a rock from their vantage point on top of the castle wall, 14 m above the moat. The rock is launched at a speed of 27 m/s and an angle of 32degrees above the horizontal.

Answer Link

danceronfire danceronfire · Answer 2 · 2017-03-13T08:08:36+01:00

Khan Academy has a really good video on this: https://m.youtube.com/watch?v=a5QnXi_lZII&ebc=ANyPxKqwT2wePxBeuoMvGuAgopefPsAAET3fCVrN7oTr7j7jOobG5sJS_Db_czLaVyZJioXM2Pt-yDUZ_tzi1nX6bCAZWTpZUQ

I'll get you started really quick (but it's way past my bedtime, so... ;)).

30 sin(28) = 14.1
30 cos(28) = 26.5

This means, when it was launched, it was launched 14.1 m/s upwards and 26.5 m/s outwards/horizontally. If you recal horizontally-launched projectile motion, there is negligible resistance (we just have to find the force of gravity against the vertical component). Calculate the time it takes by plugging in the vertical displacement into one of your mechanics equations, and then using a range/distance formula for the rest.

(The video is more helpful than I'm being at 2:08 am. Have fun and good luck!)