Guess I really need help if I can't even spell Calculus
Need a little help setting up these problems. thanks in advance
A canyon is 2000 meters deep at its deepest point. A rock is dropped from the rim above this point. Write the height of the rock as a function of time t in seconds. (Use -9.8 m/s2 as the acceleration due to gravity.)
h(t) = 1
_________
How long will it take the rock to hit the canyon floor? (Give your answer correct to 1 decimal place.)
2 s
An offshore oil rig well is 1 kilometers off the coast. The refinery is 5 kilometers down the coast. Laying pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost? Complete the following statement. (Give your answer correct to 2 decimal places.)
The pipe should be laid in the ocean from the rig to a point on the coast 1______ km from the refinery, then on land the remainder of the distance to the refinery.
For this, you need to be able to take simple integrals and understand the relationship between displacement, velocity and acceleration. So you have the acceleration, which is constant. The key step here is to know that you have a constant acceleration of -9.8 m/s, and so . So how do you find the equation for velocity, and for the distance travelled?
The answer to your next question should be fairly easy once you've found the right equations.
What equations can you build from the information provided? Remember that what you're trying to do here is to minimize the cost of the pipe. You know how to solve minimization problems, in general?