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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.

physics 
MathMate,
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/s²
use
v1²v0²=2aS
to solve for S, distance.
Add this to the 1600 m in the acceleration phase to get the maximum height. 
physics 
steve,
ewywer