A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.70s later. What was the rocket's acceleration?
Express your answer with the appropriate units.
27.49 m/s^2
To find the rocket's acceleration, we can use the kinematic equation:
d = v₀t + ½at²
where:
- d is the distance traveled (in this case, it is the distance the bolt fell)
- v₀ is the initial velocity
- t is the time traveled
- a is the acceleration
In this problem, we know that the bolt fell for 6.70 seconds, so t = 6.70s. We also know that the bolt fell under the influence of gravity, which has an acceleration of approximately 9.8 m/s².
Using the equation d = v₀t + ½at², we can rearrange it to solve for "a":
a = 2(d - v₀t) / t²
Since we are given the time the bolt fell (t) and the distance it traveled (d), we can substitute these values into the equation to find the acceleration:
a = 2(0 - v₀(6.70s)) / (6.70s)²
We know that the initial velocity of the bolt (v₀) can be considered 0 since it fell from the rocket.
Therefore, the equation simplifies to:
a = -2(6.70s) / (6.70s)²
Simplifying further, we get:
a = -2 / 6.70s
So the acceleration of the rocket is approximately -0.299 m/s². The negative sign indicates that the rocket is slowing down.