SOLUTION: A large bottle rocket is fired and launches into the air. It follows the path s(t) = t 3 + 5t where s(t) is in meters and t is in seconds. (a) We know that at 3 seconds the roc

Question 1174501: A large bottle rocket is fired and launches into the air. It follows the path s(t) = t 3 + 5t where s(t) is in meters and t is in seconds.
(a) We know that at 3 seconds the rocket is 42 feet in the air. This gives us the point (3,42). Using this point, we want to estimate the rocket's velocity. Fill out the table below, which will give us the slope of secant lines as we approaching t = 3. Clearly show your work for finding msec
t = s (t) = msec
3.1 = ? =?
3.0 = ? =?
2.99 = ? =?

(b) Using the table above, what would you predict the velocity of the rocket to be at 3 seconds?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
at t-2.99 s(2.99)=41.68
t=3.0, s(3)=42
t(3.1). s(3.1)=45.291
the slope between 2.99 and 3.0 is .32/.01 or 32 m/sec
from 3.0 to 3.1 the slope is 3,291/.1=32.91
Would predict the rocket's velocity to be 32 m/sec instantaneous velocity at 3.0 sec
one can also look at 2.999 sec
-
the derivative is 3t^2+5, which at t=3 equals 32 m/sec.
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