An archer puts a 0.300kg arrow into a bow and draws the bowstring back. She exerts an average force of 201N to draw the bow string back 1.30m. A) Assuming no frictional loss with what speed does the arrow leave the bow? B) How high will it rise if the arrow was shot straight up

Question

An archer puts a 0.300kg arrow into a bow and draws the bowstring back. She exerts an average force of 201N to draw the bow string back 1.30m. A) Assuming no frictional loss with what speed does the arrow leave the bow?                     B) How high will it rise if the arrow was shot straight up

anonymous · Answer

Please and thank you :)

sidsiddhartha · Answer

first find the acceleration of the arrow using
$$F = m × a $$
whre F = force = 201 N 
m = mass = 0.3 kg 
so $$a=\frac{ F }{ m }=270 m/s ^{2}$$
now use this 
$$v² = u² + 2×a×s $$
v = velocity at the moment the arrow leaves the bow
u = initial velocity = 0 m/s (the arrow starts from rest) 
a = acceleration = 670 m/s² 
s = displacement = 1.3 m 
so 
$$v ^{2}= 2×(670 m/s²)×(1.3 m) $$
$$v=41.3 m/s$$
 and for the second part use conservation of energy
$$\frac{ 1 }{ 2}mv ^{2}=mgh$$
so 
$$h=\frac{ v ^{2} }{ 2g }$$