Question

Please help in explaining this. dont understand at all

Answer 1

For the first minute, the rocket is traveling straight upward at a constant velocity of 600 m/s. This means that after 1 minute (60 seconds), it will have risen to an altitude of

`y=\left(600\,(\rm m)/(\rm s)\right)(60\,\mathrm s)=36000\,\mathrm m`

From this point on, it's in freefall with a starting height of 36000 m, a starting velocity of 600 m/s upward, and accelerating downward with a magnitude of 1g. At its maximum height, the rocket's velocity will be 0. We have a formula that ties all this information together:

`-\left(600\,(\rm m)/(\rm s)\right)^2=2(-g)(y_(\rm max)-36000\,\mathrm m)`

`\implies y_(\rm max)=54367\,\mathrm m\approx54000\,\mathrm m`

(rounding to 2 significant digits)

The altitude
`y` of the rocket with respect to time
`t` (AFTER the first minute) is given by

`y=36000\,\mathrm m+\left(600\,(\rm m)/(\rm s)\right)t-\frac g2t^2`

The time it takes for the rocket to reach the ground (
`y=0`) is given by

`0=36000\,\mathrm m+\left(600\,(\rm m)/(\rm s)\right)t-\frac g2t^2`

`\implies t=166.56\,\mathrm s`

which means the rocket will have spent a TOTAL time of 226.56 seconds, or approximately 230 seconds, in the air.