Monday, October 20, 2014

Projectile Motion Problems

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 sy and ay are negative. ay is also equal to g = 32.174 ft/sec²  which is an acceleration due to gravity. V0y 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 v0x is horizontal and constant, then ax is equal to zero. Therefore, the horizontal distance traveled of an object is

or