A rocket accelerates straight up from rest for 20 seconds with an acceleration of 8 m/s2. After 20 seconds the rocket motor shuts off and the rocket continues to coast upwards. How high does the rocket go in meters?

Details and assumptions
You may take the acceleration of gravity as −9.8 m/s2.
You may neglect air resistance.

Acceleration phase:

initial velocity, v0 = 0 m/s
final velocity, v1 = at = 8*20 = 160 m/s
distance, S = ut+(1/2)at² = 0 + (1/2)8(20²)
=(1/2)8(400)=1600 m

Free fall phase:
v0 = 160 m/s
acceleration,a = -9.8 m/s²
v0 = 160 m/s
v1 = 0
a = g =-9.8 m/s&sup2
use
v1²-v0²=2aS
to solve for S, distance.
Add this to the 1600 m in the acceleration phase to get the maximum height.

ewywer

To determine how high the rocket goes, we need to calculate its displacement during the acceleration phase and the coasting phase separately, and then add them together.

First, let's calculate the displacement during the acceleration phase. We know the initial velocity is 0 m/s, the time is 20 seconds, and the acceleration is 8 m/s^2. We can use the kinematic equation:

s = ut + (1/2)at^2

where:
s is the displacement,
u is the initial velocity,
t is the time, and
a is the acceleration.

Plugging in the values, we have:

s1 = (0)(20) + (1/2)(8)(20)^2
s1 = 0 + (1/2)(8)(400)
s1 = 0 + (4)(400)
s1 = 1600 meters

The displacement during the acceleration phase is 1600 meters.

Next, let's calculate the displacement during the coasting phase. The rocket is no longer accelerating, so its velocity remains constant. We can use the equation:

v = u + at

where:
v is the final velocity,
u is the initial velocity,
a is the acceleration, and
t is the time.

Since the rocket is coasting, the final velocity is 0 m/s. Therefore, we can solve for t:

0 = (0) + (8)(t)
0 = 0 + 8t
t = 0 seconds

During the coasting phase, the displacement is 0 meters since the time is 0 seconds.

Now, we need to add the displacement during the acceleration phase and the coasting phase:

Total displacement = displacement during acceleration phase + displacement during coasting phase
Total displacement = 1600 meters + 0 meters
Total displacement = 1600 meters

Therefore, the rocket goes 1600 meters high.