To find the maximum height reached by the rocket, we can use the kinematic equation that relates displacement, initial velocity, final velocity, acceleration, and time.
The equation we will be using is:
s = ut + 0.5at^2
Where:
s = displacement (maximum height)
u = initial velocity
a = acceleration
t = time
First, we need to determine the initial velocity of the rocket. We know that the rocket starts from rest on the ground, so the initial velocity is 0 m/s.
Next, we need to find the time it takes for the rocket to reach its maximum height. Given that the rocket accelerates for 11 seconds, we can use this value for the time (t) in the equation.
Now, let's plug in the values into the equation:
s = (0 * 11) + (0.5 * 23 * 11^2)
Simplifying:
s = 0 + 0.5 * 23 * 121
s = 0 + 0.5 * 2803
s = 0 + 1401.5
s = 1401.5 m
The maximum height (displacement) reached by the rocket is 1401.5 meters above the ground.
To provide the answer in units of kilometers (k), we need to convert the meters to kilometers by dividing the result by 1000:
s = 1401.5 / 1000
s = 1.4015 km
Therefore, the maximum height reached by the rocket is approximately 1.4015 km above the ground.