Question

You have designed a rocket to be used to sample the local atmosphere for pollution. It is fired vertically with a constant upward acceleration of 19 m/s2. After 20 s, the engine shuts off and the rocket continues rising (in freefall) for a while. (Neglect any effects due to air resistance.) The rocket eventually stops rising and then falls back to the ground. You want to get a sample of air that is 14 km above the ground. (a) What is the highest point your rocket reaches?

Answer 1

the highest point the rocket reaches is
`y_(max)=11,167.35meters=11.17km`

Step-by-step explanation:

Hi

First of all we are going to use
`y=(at^(2) )/(2)` while the engine is on, so
`y=(19m/s^(2)(20s)^(2)  )/(2)=3800m`.

Second, we're going to find the speed as the engine shuts off, so we have
`v=a*t=(19m/s)(20s)=380m/s`

Third, we need the time when the rocket reaches max high after engine turns off, to do that we use
`v=v_(0) -gt=380m/s-9.8m/s^(2) (t)`, then we isolate t,
`t=(380m/s)/(9.8m/s^(2) ) =38.77s`

Finally we can find highest point by using
`y=y_(0) +v_(0) *t-(g*t^(2) )/(2) =3800m+380m/s*(38.77s)-(9.8m/s^(2)*(38.77s)^(2)  )/(2)=11167.35m`