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 7.00 later.
I don't work these problems but you need to repost with the units of the 7.00. It's 7.00 what? seconds? minutes? hours?
I also note that you didn't ask a question.
To find the acceleration of the rocket, we can use the information provided. We know that the bolt falls off the side of the rocket, which means it has a purely vertical motion. Given that the bolt hits the ground 7.00 seconds later, we can use this information to determine the acceleration.
First, we need to find the time it took for the bolt to reach its maximum height. The time it takes to reach the maximum height is equal to half of the total time it takes for the bolt to hit the ground. In this case, it took 7.00 seconds for the bolt to hit the ground, so it would take half of that time to reach the maximum height, which is 3.50 seconds.
Now, we can use the formula for the time it takes to reach the maximum height in free-fall motion:
time = √(2h/g),
where h is the height and g is the acceleration due to gravity.
Since the bolt was initially at rest when it fell off the rocket, we can assume that the height from which it was dropped is equal to the height reached during its free fall. Therefore, we can use this information to solve for the acceleration due to gravity, g.
Plugging in the values we know:
3.50 = √(2h/g),
Squaring both sides of the equation, we get:
12.25 = 2h/g.
Next, we know that the bolt takes a total of 7.00 seconds to fall from its maximum height to the ground. Since this is the time it takes for an object to fall freely under gravity, we can use it to determine the value of g:
time = √(2h/g),
7.00 = √(2h/9.8),
Squaring both sides, we get:
49 = 2h/9.8.
Multiplying both sides by 9.8, we have:
h = 480.2 meters.
Now that we have determined the maximum height h, we can go back to the equation:
12.25 = 2h/g,
and substitute the values of h and solve for g:
12.25 = 2(480.2) / g,
g = 2(480.2) / 12.25,
g ≈ 78.09 m/s^2.
Therefore, the acceleration of the rocket is approximately 78.09 m/s^2.