Theres An arrow, starting from rest, it leaves the bow with a speed of 24.5 m/s.
If the average force exerted on the arrow by the bow were doubled, all else remaining the same.
so with what speed would the arrow leave the bow?
of course in m/s?
Originally Posted by rcmango
so assuming constant force while accellerating:
So assume a 1m pull on the bow, we have the time on the bow is:
and so the speed at which the arrow leaves the bow is:
Hence doubling the force increases the speed by a factor of sqrt(2).
Alternativly, work done = change in KE = force*distance.
Hence doubling the force doubles the KE, but KE is proportional to the
square of speed, so speed incread=ses by a factor of sqrt(2).