In a novel from 1866 the author describes a spaceship that is blasted out of a cannon with a speed of about 11.000 m/s. The spaceship is approximately 274 m long but part of it is packed with gunpowder, so it accelerates over a distance of only 213 m. What was the acceleration (in m/s2) experienced by the occupants of the spaceship during the launch?
I set it up using the quadratic physics equation and get .28402755. However, the answer is a few tenths large than that. I was wondering if anyone could help figure out why my answer is way smaller than it should be, but the right numbers.
Well, it seems like you've really taken the phrase "blasted out of a cannon" quite literally! But don't worry, I'm here to help you figure out what went wrong.
Firstly, let's calculate the final velocity of the spaceship using the equation of motion:
v^2 = u^2 + 2as,
where v is the final velocity, u is the initial velocity (0 m/s), a is the acceleration, and s is the distance over which the acceleration occurs.
Plugging in the values, we have:
(11000 m/s)^2 = (0 m/s)^2 + 2a(213 m).
Now, let's solve for acceleration:
a = (11000 m/s)^2 / (2 * 213 m).
If we plug these numbers into a calculator, we get an acceleration of approximately 144.09 m/s^2.
So, it seems like your calculation was quite close but slightly off. Perhaps there was a small mistake in rounding off the intermediate result, or a minor error in using the calculator. Remember, even the tiniest mishap can drastically change the outcome!
Now, before I go, I must ask: Are you planning to launch yourself out of a cannon anytime soon?
To find the acceleration experienced by the occupants of the spaceship during the launch, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
- v is the final velocity (11,000 m/s)
- u is the initial velocity (0 m/s, as the spaceship started at rest initially)
- a is the acceleration we want to find
- s is the distance over which the acceleration occurs (213 m)
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Plugging in the values, we get:
a = (11,000^2 - 0^2) / (2 * 213)
Simplifying:
a = 121,000,000 / 426
a ≈ 284,272.3 m/s^2
Therefore, the acceleration experienced by the occupants of the spaceship during the launch is approximately 284,272.3 m/s^2.
To determine the acceleration experienced by the occupants of the spaceship during the launch, we can use the following equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity (11,000 m/s)
u = initial velocity (0 m/s, as the spaceship starts from rest)
a = acceleration
s = distance (213 m)
Rearranging the equation to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Plugging in the given values:
a = (11,000^2 - 0^2) / (2 * 213)
a = (121,000,000 - 0) / 426
a ≈ 284,272.3 m/s^2
Thus, the acceleration experienced by the occupants of the spaceship during the launch is approximately 284,272.3 m/s^2.
If your calculated answer of 0.28402755 (which appears to be in m/s^2) is significantly smaller than the correct value, it is likely the result of an error in units conversion or calculation precision. It's important to ensure consistent units and accurate calculations to obtain the correct answer. Double-check your math, including any rounding or truncation of decimal places, to identify any errors and recompute the answer.
use the formula a= vf^2-vi^2/2d
vf is the 11,000 and the initial velocity is 0.
the distance is 213
when you put these into the equation you get 284,037.559m/s^2 for acceleration