an archer shoots an arrow into a piece of wood. the arrow is traveling at 120km/h when it strikes the wood. the arrow penetrates 3.8cm into the wood before stopping. what is its average acceleration (in m/s squared) into the wood?
You need an equation of motion
v^2 = u^2 + 2aS
v = final velocity
u = initial velocity
a = acceleration
s = displacement
Watch your units. The velocity is in km/h and your displacement is in cm and you want the answer in m/s^2
To find the average acceleration of the arrow into the wood, we first need to convert the speed from km/h to m/s.
1. Convert the speed from km/h to m/s:
- 1 km/h = 1000 m/3600 s (conversion factor)
- 120 km/h = (120 * 1000) / 3600 m/s
- 120 km/h ≈ 33.33 m/s
Now that we have the speed in m/s, we can calculate the acceleration using the formula for average acceleration:
average acceleration = (final velocity - initial velocity) / time
In this case, the initial velocity is 0 (since the arrow starts from rest) and the final velocity is 33.33 m/s (the speed at which the arrow strikes the wood). So the equation becomes:
average acceleration = (33.33 m/s - 0 m/s) / time
Now we need to calculate the time it takes for the arrow to penetrate the wood. For this, we need to know the distance the arrow travels.
Given that the arrow penetrates 3.8 cm into the wood, we can convert this to meters:
1 cm = 0.01 m
So, the distance traveled by the arrow is 3.8 cm * 0.01 m/cm = 0.038 m.
Therefore, the final equation to find the average acceleration becomes:
average acceleration = (33.33 m/s - 0 m/s) / time = 33.33 m/s / time
To solve for time, we rearrange the equation to:
time = 0.038 m / (33.33 m/s)
Now we can calculate the time it takes for the arrow to penetrate the wood:
time = 0.038 m / 33.33 m/s ≈ 0.0011 s
Finally, we can substitute the value of time back into the original equation to find the average acceleration:
average acceleration = 33.33 m/s / 0.0011 s ≈ 30300 m/s²
Therefore, the average acceleration of the arrow into the wood is approximately 30300 m/s².