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**1. Homework Statement**

A rocket is red vertically with an acceleration of 250 m/s2. After 30 seconds, the

rocket's motor shuts o. Find the maximum altitude achieved by the rocket and the

total time from take-o to return to the surface of the earth, assuming that the rocket's

design makes air resistance negligible.

**2. Homework Equations**

**3. The Attempt at a Solution**

d^2x/dt=a=acceleration.

dx/dt=at+c = velocity=v(t)

v(0)=0 implies c=0 so v(t)=at

x(t)=1/2*a*t*t +d. x(0)=0 implies d=0 so x(t)=x(t)=1/2*a*t*t

x(t)=(1/2)*a*t*t=1/2 * (250)*30*30=112500 meters

112500=1/2 * 9.8 * t$ *t$. where t$ is the time it takes to return to earth.

t$= 151.52 secs

total time is t +t$=181.52 secs.

Is this right? My classmates did it differently but I do not understand how I am wrong. please help!!!!!