A test rocket is fired straight up from rest with a net acceleration of 20 m/s2. After 4 seconds the motor turns off, but the rocket continues to coast upward. What maximum elevation does the rocket reach?
I know the answer is 487m but I’m not sure as to how to do this.
Steps Please, Thanks!
2 Answers

Well, here’s one way to do it…
The rocket’s motor cuts out at an altitude of 160 meters.
4^2 * 20 / 2 = 160
The rocket now has velocity of 80 m/s.
4 * 20 = 80
It then begins to decelerate at a rate of 9.8 m/s/s, and will reach it’s maximum altitude 8.163 seconds later.
80 / 9.8 = 8.163
During this 8.163 second time interval the rocket will climb an additional 326.531meters.
8.163^2 * 9.8 / 2 = 326.531
…for a total height of 486.531 meters.

a) for the duration of the 1st a million.7 s after liftoff you mentioned that we’ve an acceleration of sixteen.0 m/s^2 (interior the upward course needless to say). for this reason from newtons regulation: F = ma so we are in a position to declare (assuming that the mass of the rocket gasoline is negligible): F = [(84g)/(1000g/kg)]*sixteen.0m/s^2 = a million.344 N [upwards] b) The rigidity exerted on the rocket via the burning gasoline is area of the internet rigidity. to that end we’ve gravity working interior the downward course and the burning of the rocket gasoline propelling the rocket up. for this reason from the internet rigidity, which we only found out to be a million.344 N (up) we are in a position to declare: a million.344 N (up) = rigidity via capacity of Burning of gasoline (up) – rigidity of Gravity (down) a million.344 N (up) + rigidity of Gravity (down) = rigidity via capacity of Burning of gasoline (up) a million.344 N (up) + (0.84g)/(1000 g/kg)*9.8 m/s^2 = rigidity via capacity of Burning of gasoline (up) a million.3358 N (up) = rigidity via capacity of Burning of gasoline (up) c) After the gasoline became spent, there is now only gravity engaged on the rocket interior the downwards course. for this reason internet rigidity to that end = rigidity of gravity = 0.80 4 grams * a million/1000 g/kg * 9.8 m/s^2 = 0.008232 N. d) This one i’m no longer particularly confident on, i’ll go away this area to somebody else. keep in mind however, all of this is assuming the rocket gasoline weighs zilch.