The length of arc in rectangular coordinates is given by the following formulas:

See the derivations here: http://www.mathalino.com/reviewer/integral-calculus/length-arc-xy-plane…
 

Problem
An airplane flew from Davao City whose latitude is 14° N and longitude of 121.5° E on a course of S 30° W and maintaining uniform altitude. At what longitude will the plane cross the equator?
A. 110° 30' East
B. 122° 26' East
C. 113° 33' East
D. 116° 11' East
 

Problem
Gas is escaping from a spherical balloon at the rate of 2 cm³/min. Find the rate at which the surface area is decreasing, in cm²/min, when the radius is 8 cm..
 

Problem 01
A 5-m line AD intersect at 90° to line BC at D so that BD is 2 m and DC = 3 m. Point P is located somewhere on AD. The total length of the cables linking P to points A, B, and C is minimized. How far is P from A?
 

Problem 859
Determine the value of EIδ under P in Fig. P-859. What is the result if P is replaced by a clockwise couple M?
 

Problem
Chords AB and AC are drawn on a circle of radius 10 inches. Find the angle between the chords if the arc BAC is 28 inches long.
 

Problem 01
Determine the equation of the curve such that the sum of the distances of any point of the curve from two points whose coordinates are (–3, 0) and (3, 0) is always equal to 8.
 

Problem 02
A bullet is fired at an initial velocity of 150 m/s and an angle of 56° at the top of a 120 m tall building. Neglecting air resistance, determine the following:

1. The maximum height above the level ground that can be reached by the bullet.
2. The time for the bullet to hit the ground.
3. The velocity with which the bullet will hit the ground.

Moment distribution is based on the method of successive approximation developed by Hardy Cross (1885–1959) in his stay at the University of Illinois at Urbana-Champaign (UIUC). This method is applicable to all types of rigid frame analysis.
 

Problem
A circle of radius r rolls along a horizontal line without skidding.

1. Find the equation traced by a point on the circumference of the circle.
2. Determine the length of one arc of the curve.
3. Calculate the area bounded by one arc of the curve and the horizontal line.