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 6.50 s later.
Sorry, the question is: What was the rocket's acceleration?
To find the acceleration of the rocket and the height it reached before the bolt fell off, we need to break down the problem into two parts: the motion of the rocket before the bolt falls off and the motion of the bolt after it falls off.
1. Motion of the rocket before the bolt falls off:
Since the bolt falls off after 4 seconds and hits the ground 6.50 seconds later, we can calculate the time it took for the bolt to fall after it was released:
Time for the bolt to fall = 6.50 s - 4 s = 2.50 s
Since the motion of the rocket and the bolt fall are related, we can consider the bolt's fall as the time it would take for an object dropped from the same height to reach the ground. Therefore, we can use the equation for free-fall motion:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken for the object to fall (2.50 s).
To find the height the bolt fell from, substitute the given values into the equation:
h = (1/2) * 9.8 m/s^2 * (2.50 s)^2
2. Motion of the rocket after the bolt falls off:
To find the acceleration of the rocket, we can use the equation of motion:
d = v0 * t + (1/2) * a * t^2
where d is the distance traveled, v0 is the initial velocity, t is the time, and a is the acceleration.
We know that the bolt fell off 4 seconds after liftoff, so the rocket was accelerating for 4 seconds before the bolt fell off. The distance traveled during this time is given by the equation:
d = v0 * t + (1/2) * a * t^2
Substituting the given values, d = 0 (since the rocket is at the same position as the initial position), t = 4 s, and solving for a gives us the acceleration of the rocket.
Once we have the acceleration, we can use the equation of motion to find the height reached by the rocket before the bolt fell off:
h = v0 * t + (1/2) * a * t^2
Please provide the initial velocity (v0) of the rocket, and I can help you calculate the height it reached and the acceleration.