Final answer:
To find the vertical distance covered and final velocity during the fuel burn phase, use the equations Δy = v₀t + 1/2at² and v = v₀ + at, respectively. After fuel depletion, assuming a deceleration of 10 m/s², use the equation h = (v² - u²) / (2a) to estimate the maximum height the rocket reaches.
Step-by-step explanation:
To solve this problem, we need to break it down into two parts: the fuel burn phase and the post-fuel depletion phase.
a. During the 2.0s fuel burn, we can calculate the vertical distance covered by using the equation:
Δy = v₀t + 1/2at²
Where Δy is the vertical distance, v₀ is the initial velocity, t is the time, and a is the acceleration.
The rocket starts from rest, so its initial velocity is 0 m/s. The time is 2.0 s and the acceleration can be calculated using the equation:
a = (F/m) - g
Where F is the thrust force, m is the mass of the rocket, and g is the acceleration due to gravity. Plugging in the given values, we can calculate the acceleration. Finally, we can substitute the values into the equation for Δy to find the vertical distance covered.
For the final velocity, we can use the equation:
v = v₀ + at
Where v is the final velocity. Plugging in the values, we can calculate the final velocity.
b. After fuel depletion, assuming a deceleration of 10 m/s², we can calculate the maximum height the rocket reaches using the equation:
h = (v² - u²) / (2a)
Where h is the maximum height, v is the final velocity (obtained from part a), u is the initial velocity (0 m/s), and a is the deceleration. Plugging in the values, we can calculate the maximum height the rocket reaches.