A rocket moves upward, starting from rest with an acceleration of 28.4 m/s2 for 4.79 s. It runs out of fuel at the end of the 4.79 s but does not stop. How high does it rise above the ground?
See previous post.
To find the height the rocket rises above the ground, we need to use the equations of motion.
The first equation we can use is the formula for displacement:
s = ut + (1/2)at^2
Where:
s = displacement (height)
u = initial velocity (0 m/s since the rocket starts from rest)
t = time (4.79 s)
a = acceleration (28.4 m/s^2)
Since the rocket starts from rest, the initial velocity is 0 m/s. Therefore, the equation simplifies to:
s = (1/2)at^2
Plugging in the given values:
s = (1/2)(28.4 m/s^2)(4.79 s)^2
Now, let's calculate the height:
s = (1/2)(28.4)(22.96)
s ≈ 650.42 m
Therefore, the rocket rises approximately 650.42 meters above the ground.