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.
The Attempt at a Solution
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!!!!!