posted by Caleb on .
While standing on an open bed of a truck moving at 35 m/s, and archer sees a duck flying directly overhead. The archer shoots an arrow at the duck and misses. The arrow leaves the bow with a vertical velocity of 98 m/s.
a) how long does it remain in the air
b) the truck maintains a constant speed of 35 m/s and does not change it's direction. Where does the arrow finally land?
c) what horizontal distance does the arrow travel while its in the air?
Well first of all, the arrow hits the archer on the way down. Both the truck and the archer have a constant horizontal velocity component of 35 m/s. Your late archer deserved it no doubt
now the vertical problem.
Vi = 98
v = Vi - 9.8 t
0 at top
98 = 9.8 t
t = 10 seconds to top (good archer, strong bow)
a) 20 seconds up and down
b) did that, archer dead in truck bed. always turn after dropping a bomb out of your airplane by the way.
c) 20 seconds at 35 m/s = 700 meters
you are, of course, assuming that there was no horizontal component to the arrow's velocity.
In Heinlein's "Stranger in a Strange Land" there is a character who is a professional observer. If you point to a house on a hill and ask what color it is, he'll reply, "This side is white," making no assumptions about the other sides.
However, given the usual sloppy problems posted here, I agree with your analysis (ignoring air resistance).
This dead archer was a dead shot and the duck was directly overhead :) By the way it was an expert seagull pulling out of a bombing run anyway and the archer was simply retaliating.