How Is Average Acceleration Calculated for an Arrow on a Bow?

[Combine]

Homework Statement

I will just try to post the whole questions, maybe my idiot eyes missed something...

an arrow is accelerated for a displacement of 75cm [fwd]
while it is on the bow, if the arrow leaves the bow at a velocity of 75m/s [fwd]
what is it's average acceleration while it's on the bow

Homework Equations

t = displacement/ velocity
a = velocity/time

The Attempt at a Solution

75 cm -> .75
0.75 / 75 = 0.01s
disp = 75m

t = 75/0.75 = 100s
velocity = 75m/s

a = velocity / time
time = displacement + velocity / velocity
acceleration = velocity/(disp/velocity) = vecloity / 0.01 = 7500 WTH??

 

[SteamKing]

The arrow leaves the bow with a velocity of 75 m/s, but its initial velocity = 0 m/s

 

[Combine]

ya it should be, according to logic I guess lol
just I've been having a lot of trouble trying to figure out the average acceleration

 

[PhanthomJay]

ya it should be, according to logic I guess lol
just I've been having a lot of trouble trying to figure out the average acceleration

Average acceleration is the change in velocity divided by the change in time. You are not given the time. So you must assume a linear variation of acceleration while the arrow is in contact with the bowstring (it behaves like a spring), in which case you can use the standard kinematic equations to solve for the average acceleration.

 

[rwisz]

I would approach this problem by first clarifying the units used in the question. The displacement of the arrow is given in centimeters, while the velocity is given in meters per second. It is important to use consistent units in calculations to ensure accuracy.

Assuming the displacement of the arrow is actually 75 meters instead of 75 centimeters, we can calculate the average acceleration using the formula a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time. In this case, vf = 75 m/s, vi = 0 m/s, and t = 0.01 s.

Thus, the average acceleration of the arrow while it is on the bow is 7500 m/s^2. This is a very high acceleration, which is to be expected since the arrow is accelerated to a high velocity in a short amount of time. It is important to note that this acceleration is only applicable while the arrow is on the bow and does not take into account any other forces acting on it after it leaves the bow.

To summarize, the average acceleration of the arrow while it is on the bow is 7500 m/s^2, assuming the displacement is 75 meters and the velocity is 75 m/s. It is important to use consistent units and clarify any uncertainties in the question to obtain an accurate solution.