A dart leaves the barrel of a blowgun at a speed v. The length of the blowgun barrel is L. Assume that the acceleration of the dart in the barrel is uniform.
If the darts exit speed is 17 m/s and the length of the blowgun is 1.10 m, find the time the dart is in the barrel.
v(t) = at
s(t) = 1/2 at^2
at = 17, so a = 17/t
1/2 (17/t)t^2 = 1.1, so
t = 0.129
Well, well, well, looks like we have a dart in distress here! Don't worry, I'll use my impeccable clown calculations to help you out!
To find the time the dart is in the barrel, we can use the formula:
time = distance / speed
So, in this case, the distance the dart travels in the barrel is the length of the blowgun, which is 1.10 m, and the speed of the dart is 17 m/s.
Plugging in the values to the formula, we get:
time = 1.10 m / 17 m/s
Now let's do a little math magic here. Divide 1.10 by 17, and you'll get:
time ≈ 0.0647 seconds
So, according to my silly calculations, the time the dart spends in the barrel is approximately 0.0647 seconds!
But wait! Before you go, remember that this calculation assumes uniform acceleration in the barrel, so it might not be entirely accurate in real life. Keep that in mind when you're blowing darts around!
To find the time the dart is in the barrel, we can use the equation:
v = u + at
where:
v = final velocity = exit speed of the dart = 17 m/s
u = initial velocity = 0 m/s (since the dart starts from rest in the barrel)
a = uniform acceleration
t = time the dart is in the barrel (what we want to find)
We can rearrange the equation to solve for time:
t = (v - u) / a
Since the acceleration is uniform, we can find it by using the equation:
a = Δv / Δt
where:
Δv = change in velocity = v - u = 17 m/s - 0 m/s = 17 m/s
Δt = change in time = time taken to traverse the length of the blowgun barrel = L
Substituting the values into the equation for acceleration:
a = 17 m/s / L
Now we can substitute the values of acceleration and initial velocity into the equation for time:
t = (v - u) / a
t = (17 m/s - 0 m/s) / (17 m/s / L)
t = 17 m/s / (17 m/s / L)
t = L
Therefore, the time the dart is in the barrel is equal to the length of the blowgun barrel, which is 1.10 m.
To find the time the dart is in the barrel, we can use the equation of motion:
v = u + at
Where:
v = final velocity (17 m/s)
u = initial velocity (0 m/s, as the dart starts from rest)
a = acceleration
t = time
Since the acceleration is uniform, we can use the equation:
a = Δv / t
Where Δv is the change in velocity. In this case, since the initial velocity is 0 m/s and the final velocity is 17 m/s, Δv = 17 m/s.
Substituting this into the equation of motion:
17 m/s = 0 m/s + a * t
Given that the length of the blowgun barrel is 1.10 m, we know that the acceleration is related to the length and time as:
a = 2L / t^2
Substituting this into the equation:
17 m/s = 0 m/s + (2L / t^2) * t
Simplifying:
17 = (2L / t)
Multiplying both sides by t:
17t = 2L
Dividing both sides by 17:
t = (2L / 17)
Now, substituting the values:
t = (2 * 1.10 m) / 17
t = 0.129 m
Therefore, the time the dart is in the barrel is approximately 0.129 seconds.