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

Answer:

the highest point the rocket reaches is $y_{max}=11,167.35meters=11.17km$

Explanation:

Hi

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

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, $t=\frac{380m/s}{9.8m/s^{2} } =38.77s$

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