The three pigls are building their houses while the brik=ck house building pig and the stick house building pig are working at a steady rate, the straw house building pig(knowing the wolf will arrive first at his house) is frantically increasing his rate of building by 2feet/minute. the straw house building pig has to make his house 16 ft tall(right now, it's 0 feet tall) and the wolf is scheduled to arrive in 5 minutes. Will the pig have his house built for the wolf to blow down by the time he arrives?
are you sure this is a question?
this is just a standard acceleration problem.
s = 1/2 at^2
16 = 1/2 * 2 * t^2
16=t^2
t=4
so, in 4 min the house will be 16' tall, and he will be (briefly) safe.
now, if you want to use your calculus, let f(t) be the height of the house after t minutes.
f ''(t) = 2
f '(t) = 2t + c
f '(0) = 0 means c=0 and
f '(t) = 2t
f(t) = t^2+c
f(0) = 0 means c=0, so
f(t) = t^2
16 = t^2
t=4
To determine whether the pig will have his house built by the time the wolf arrives, we need to calculate how long it will take the pig to build his house given his increasing rate of building.
Currently, the pig's house is 0 feet tall, and he needs to build it to be 16 feet tall. The pig is increasing his building rate by 2 feet per minute.
Let's calculate the time it will take for the pig to reach 16 feet:
1. For the first minute, the pig builds 2 feet (since his rate has increased to 2 feet per minute).
2. For the second minute, the pig builds an additional 4 feet (2 feet per minute rate multiplied by 2 minutes).
3. For the third minute, the pig builds an additional 6 feet (2 feet per minute rate multiplied by 3 minutes).
4. For the fourth minute, the pig builds an additional 8 feet (2 feet per minute rate multiplied by 4 minutes).
5. For the fifth minute, the pig builds an additional 10 feet (2 feet per minute rate multiplied by 5 minutes).
By the end of the fifth minute, the pig will have built a total of 30 feet (2 + 4 + 6 + 8 + 10 = 30 feet).
Since the pig only needs to build his house to be 16 feet tall, he will have finished building his house for the wolf to blow down before the wolf arrives.