Length of Arc in XY-Plane | Applications of Integration

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

$\displaystyle s = \int_{x_1}^{x_2} \sqrt{1 + \left( \dfrac{dy}{dx} \right)^2} \, dx$   and   $\displaystyle s = \int_{y_1}^{y_2} \sqrt{1 + \left(\dfrac{dx}{dy} \right)^2} \, dy$

 

length-of-arc-xy-plane.jpg

 

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

02 - Bullet fired from the top of a building

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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.

 

02-bullet-from-top-building.gif

 

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