Riding Roller coasters are a exciting and thrilling way to spend your day. Although, you may have many questions about them, for instance how is a roller coaster is built? we will try to answer this question using calculus.
Abu Butt April 10, 2014
Title: Where should a pilot start descent?
Abstract: In our project, we are trying to find out where should a pilot start to land/ descent. The pilot will start at a certain height. Our goal is to find out the speed, height, and length of the runway, from where an airplane should start landing. We will use knowledge of calculus to solve this problem.
Introduction: The cruising Altitude is h when descent starts at a horizontal distance l from touching down at the origin.
The pilot must maintain a constant horizontal speed v throughout descent.
The absolute value of the vertical acceleration should not exceed a constant k ( which is much less than the acceleration due to gravity)
Take the derivative of the equation P(x)=ax3+bx2 with respect to time (t)
(dx/dt) being with respect to time, replace (dx/dt) with (-v). Where (-v) stands the horizontal velocity
Find the derivative again
Substitute a, and b that were found in the previous problem
Abu Butt April 9, 2014
Where should a pilot start descent?
In our project, we are trying to find out where should a pilot start to land
/descent. The pilot will start, [starting] at a certain height. During a certain time of period, the velocity of an airplane will change according to distance from the runway. The formula to calculate the velocity is V = d/t. Our goal is to find out the speed, height, and length [distance] of [from] the runway, from where an airplane should start landing. As we know, the pilot wants to descent at the polynomial of x3, and k is constant. We will use knowledge of calculus to solve this problem.