A model rocket blasts off and moves upward with an...

A model rocket blasts off and moves upward with an acceleration of 13 m/s^2 until it reaches a height of 27 m, at which point its engine shuts off and it continues its flight in free fall. a) What is the maximum height attained by the rocket? b) What is the speed of the rocket just before it hits the ground? c) What is the total duration of the rocket's flight?

Transcript

00:01 We have a question in this a model rocket blast of and moves upward with an acceleration of 13 meter per second square initial acceleration was 13 meter per second square until it reaches a height of 27 so up to here up to that height or let us say like this yes up to this height acceleration is 13 meter per second square 13 meter per second square and this height is 27 meters at which point it then shuts off and continues its flight in free fall okay so what is the maximum height is in by the rocket what is the speed of the rocket just before it fits the ground and what is the total duration of rocket's flight so let us say from a to b it is rocket now from b onwards it will start free fall okay so we need to first find a speed at this point speed at point b upward with acceleration initial speed was no worries we have to find final speed so we have acceleration we have a height so we will be using the formula v equal to u plus 80 so v equal to you will be assumed to be zero and 80 13 okay so we do not have time we do not have time we will be using b sq equal to u s square plus 2 as from here you will be 0 so we will be under root 2 as 2 into 13 into 27 that would be 2 into 27 that would be 2 into 13 into 27 702 and that's 2 so b s v equal to under 7 hundred to 26 .49 meter per second it is speed at one feet now it will start free fall and up to maximum height here let us say v dash becomes equal to zero initially u is this so height in this case because g will now be acting vertically downward so in this case v square will be using v square equal to u s minus 2 g h so final should be 0 initial will be this so 702 minus 2 into 9 .8 into h will be 702 by 2 into 9 .8 that would be 702 divided by 19 .6 so 35 .8 meters so this would be height h would be 35 .8 meters.

03:29 Okay, so maximum height in this case maximum height will be 27 height, 27 meters when engine was working and 35 .8 meters when engine was shut off...

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