A new SpaceX rocket is being tested and launches from the ground. The first stage rocket engine provides constant upward acceleration during the burn phase. After the first stage engine burns out, the rocket has risen to 105.0 m and acquired an upward velocity of The second stage fails to fire. The rocket continues to rise, reaches maximum height, and falls back to the ground. Neglect air resistance. The time interval during which the rocket engine provided the upward acceleration, is closest to

A. 3.0 s.

B. 4.2 s.

C. 1.5 s.

D. 1.7 s.

E. 4.0 s.

To find the time interval during which the rocket engine provided the upward acceleration, we can use the equations of motion.

Given:
Initial velocity, u = 0 m/s (since the rocket starts from rest)
Final velocity, v = ?? (not provided)
Acceleration, a = constant (not provided)
Distance traveled, s = 105.0 m

We need to find the time interval, t.

First, let's consider the motion during the burn phase of the first stage. The rocket starts from rest and reaches an upward velocity before the first stage engine burns out. We can use the equation of motion:

v = u + at

Since the velocity starts from 0 m/s, we can simplify the equation to:

v = at

Now, let's find the velocity at burnout and the time interval during the burn phase.

Given:
Final velocity at burnout, v = ?? (not provided)

v = at

105.0 m/s = a * t

Now, we need to find the value of 'a' to solve for 't'. Let's consider the motion during the entire ascent phase of the rocket (before it reaches maximum height).

The rocket starts from rest and achieves a certain maximum height while experiencing constant upward acceleration.

To find the maximum height, we can use the equation of motion:

v^2 = u^2 + 2as

Since the initial velocity is 0 m/s and the rocket reaches maximum height, the equation simplifies to:

v^2 = 2as

Now, let's substitute the given values:

105.0 m/s^2 = 2a(105.0 m)

Simplifying the equation:

a = 105.0 m/s^2 / (2 * 105.0 m)

a = 0.5 m/s^2

Now that we have found the value of 'a', we can substitute it back into the equation:

105.0 m/s = (0.5 m/s^2) * t

Simplifying the equation:

t = 105.0 m/s / 0.5 m/s^2

t = 210.0 s

Therefore, the time interval during which the rocket engine provided the upward acceleration is 210.0 seconds.

However, in the answer choices given, there is no option close to 210.0 s. Therefore, it seems like there may be a mistake or missing information in the question.