- We're told the graph at left in the ta- plane approximates the Apollo 8's altitude, a, in kilometers, t seconds after lift-off. What was the approximate rate of change of the altitude of Apollo 8 between 156 and 184 seconds after lift-off. So, pause this video and
try to figure that out. Alright, now let's do this together. So if you wanna figure out the approximate rate of change of a with respect to t our approximate rate of change of altitude over this time what we would wanna do is we would say all right what was our change in altitude over our change over our change in time and we know what our change in time is we go from 156 seconds to 184 seconds so the change in time right over here this is going to be 184 seconds minus 156 seconds and then what is our change in altitude over that same time period. So, when we go from 156 seconds to 184 seconds, our altitude goes from 70 to 96. So, Apollo 8 has gone up by 26 kilometers. So our change in altitude is 96 minus 70 and so what do we get? Our numerator 96 minus 70 that is 26 kilometers over how much time? Over 184 minus 56 Let's see 86 minus 56 would be 30 so this is going to be 28 seconds over 28 seconds Now, we could rewrite this as 26 over 28 kilometers per second and we could try to calculate this but this is multiple choice so we could really try to approximate which of these choices is 26 over 28 Well we know that this value is going to be a little bit less than one and so the only choice
here that is a little bit less than one is choice A we are done 0.93 kilometers per seconds we know that it's not B because that's more than one And 26 way more than one and 28 is even more even wayer more (laughs) than one. So, so we feel good about choice A.