an anchor shoots an arrow into a piece of wood. the arrow is traveling at 120 km/h when it strikes the wood. the arrow penetrates 3.8 cm into the wood before stopping. what is the average acceleration (in m/s^2) into the wood?

first convert 120 km/hr into m/s

120 km/hr(1000 m/km)(1 hr /3600 s) = 33.3 m/s
It drops from 120 to zero so during the stop it averaged 33.3/2 m/s = 16.65 /s SPEED
it went .038 meters at average speed of 16.65 so it took .038 m /16.65 m/s = .00228 seconds to stop.
so change in speed/change in time = (0 - 33.3) / .00228
= -14605 m/s^2

To find the average acceleration, we need to use the formula:

acceleration = (final velocity - initial velocity) / time

Since we are given the initial velocity and final velocity, we can use these values to find the acceleration.

Given:
Initial velocity (u) = 120 km/h = 120,000 m/3600 s = 33.33 m/s
Final velocity (v) = 0 m/s (when the arrow stops)
Distance (s) = 3.8 cm = 0.038 m

We know the distance traveled, but we need to find the time it takes to travel this distance.

We can use the equation s = ut + (1/2)at^2, where s is the distance, u is the initial velocity, a is the acceleration, and t is the time.

Plugging in the values, we get:

0.038 m = (33.33 m/s)t + (1/2)a(t^2)

Since the arrow comes to rest, the final velocity is 0, so we can simplify the equation to:

0.038 m = (33.33 m/s)t

Now, solve for time (t):

t = 0.038 m / 33.33 m/s = 0.00114 s

Now substitute the values into the initial formula to find the acceleration:

acceleration = (0 - 33.33 m/s) / 0.00114 s

acceleration ≈ -29,236.84 m/s²

Therefore, the average acceleration of the arrow into the wood is approximately -29,236.84 m/s².

To find the average acceleration of the arrow into the wood, we need to determine the change in velocity and the time taken.

Here's how we can do it step by step:

Step 1: Convert the initial velocity from km/h to m/s.
Since the arrow's velocity is given in kilometers per hour (km/h), we need to convert it to meters per second (m/s).

To convert km/h to m/s, divide the velocity by 3.6, because there are 3.6 meters in one second.

120 km/h ÷ 3.6 = 33.333 m/s (rounded to three decimal places)

So, the initial velocity of the arrow is 33.333 m/s.

Step 2: The final velocity of the arrow will be 0 m/s since it stops.

Step 3: Calculate the change in velocity.
The change in velocity is the final velocity minus the initial velocity.

Change in velocity = 0 m/s - 33.333 m/s = -33.333 m/s

However, since we are interested in the magnitude of the acceleration (which is always positive), we can take the absolute value.

Change in velocity = |-33.333 m/s| = 33.333 m/s

Step 4: Determine the time taken.
The time taken is not given in the question, so we need to find it using the information provided.

To do that, we make use of the formula for average acceleration:

Average acceleration = change in velocity / time taken

Since we have the change in velocity, we need to calculate the time taken.

To determine the time, divide the distance penetrated by the velocity.
Distance = 3.8 cm = 0.038 m

Time taken = Distance / Velocity

Time taken = 0.038 m / 33.333 m/s = 0.00114 s (rounded to five decimal places)

Step 5: Calculate the average acceleration.
Now that we have both the change in velocity (33.333 m/s) and the time taken (0.00114 s), we can calculate the average acceleration.

Average acceleration = change in velocity / time taken

Average acceleration = 33.333 m/s / 0.00114 s = 29210.526 m/s^2 (rounded to three decimal places)

Therefore, the average acceleration of the arrow into the wood is approximately 29210.526 m/s^2.