hi could somebody confirm my answers for ux, uy and t
A cannon ball is fired at 40 degrees to the horizontal fro mthe top of a 218.7 m cliff and hits
a taret 300m from the base of the cliff
surfing says the answers are
ux=30.64 ms-1
uy=25.7ms-1
t=9.8 secs
ignore the massive cross through my answer
Think the answers from surfing are correct.
delta(x) = vtcos(40) = 300 - so, by rearranging, t = 300/(vcos(40)) when the range is achieved (when the ball hits the ground).
Then, sub this value of t into the the quadratic for delta(y) of form - delta(y) = -1/2at^2 + vsin(40) + 218.7
Allowing this quadratic to be = to 0 (as, when the ball has achieved the range of 300m, the vertical displacement of the projectile will be 0 (or -218.7m; depending on how you set up the quadratic initially)) proceed to solve for 'v'.
I had v^2 = 1597.481175... so v = 39.96850228
so uy = vsin(40) = 39.97 x sin(40) = 25.69 m/sec
and ux = vcos(40) = 39.97 x cos(40) = 30.62 m/sec
Then, for the time of flight, I just subbed the aforementioned 'v' back into the initial quadratic for delta(y), letting it = 0 (i.e. delta(y) = 0 since when the time of flight is achieved, the projectile reaches the ground); solving it with the quadratic formula.
You should get two values for t (the positive value being the one you want as t>0), one of them being 9.798270249... secs.
Hope this helps.