A rocket moves upward, starting from rest with an acceleration of 30.5 m/s2 for 3.39 s. It runs out of fuel at the end of the 3.39 s but does not stop. How high does it rise above the ground?
To find the height the rocket rises above the ground, we can use the kinematic equation:
h = v₀t + (1/2)at²
where:
h = height above the ground
v₀ = initial velocity (which is 0 because the rocket starts from rest)
t = time
a = acceleration
Given:
v₀ = 0 m/s (starting from rest)
t = 3.39 s
a = 30.5 m/s²
Substituting the values into the equation:
h = (0)(3.39) + (1/2)(30.5)(3.39)²
Simplifying the equation:
h = 0 + (1/2)(30.5)(11.4921)
h = (1/2)(30.5)(11.4921)
h ≈ 174.26 meters
Therefore, the rocket rises to a height of approximately 174.26 meters above the ground.