__Category__: Mechanics, Physics"Published in Newark, California, USA"

An object falls from a plane flying horizontally at an altitude of 40,000 ft. at 500 mi/hr. How long will it take to hit the ground? What is the horizontal distance traveled of an object?

__Solution__:

The given problem is about projectile motion in which an object is thrown from its maximum height with an initial velocity. The projectile curve is a half-parabola as shown in the figure below

Photo by Math Principles in Everyday Life |

First, let's consider the y-component of an object in order to calculate the time required to hit the ground. From the distance formula

Since an object is thrown in a downward position, then the values of s

_{y}and a

_{y}are negative. a

_{y}is also equal to g = 32.174 ft/sec² which is an acceleration due to gravity. V

_{0y}is zero because the direction of initial velocity of an object is horizontal. Therefore, the time required of an object to hit the ground is

Next, let's consider the x-component of an object in order to calculate the horizontal distance traveled of an object. From the distance formula

Since the direction of v

_{0x}is horizontal and constant, then a

_{x}is equal to zero. Therefore, the horizontal distance traveled of an object is

or