00:01
So let's say we have a rocket with an acceleration of 12 meters a second squared upwards.
00:10
And it accelerates at this rate until it reaches a height of 26 meters after which the engine shuts off and it falls back down.
00:20
So part a asks, what is the maximum height attained by the rocket? so the maximum height is going to be 26 meters plus the additional height achieved by the rocket.
00:36
So one half, we'll call this at squared.
00:38
And what is t? we don't know t yet, but t is the time it takes to reach this maximum height, and t is the time at which the velocity is zero.
00:47
So t is going to be maybe an easier way of writing this would be like v squared over to where v is the velocity it has.
00:59
Has when the engine's cut off.
01:01
So that would be the acceleration times the time it spins accelerating.
01:05
And we can figure that out because what we have is 26 meters is equal to one half a times that time interval squared.
01:12
So t that we're looking for is going to be two times 26, so 52 meters divided by 12 meters a second.
01:20
And then we take the square root.
01:23
So this is about 2 .08 seconds.
01:27
And that means the velocity at that point is going to be 12 meters a second squared times 2 .8 or 08 seconds.
01:37
And so this is about 25 meters a second.
01:42
All right.
01:43
And so that means our maximum height is going to be 26 meters plus 25 meters a second squared over 2g...