Falling Body Problem

    Another type of rectilinear motion is the free-falling body problem.  

Proposition (Falling Body Problem) The position of a free-falling body (neglect air resistance) under the influence of gravity can be represented by the function



where is the acceleration due to gravity (on earth ) and and are the initial height and velocity of the object (when ).

Example (Falling Object Problem) A ball is thrown vertically upward from the ground with an initial velocity of 160 ft/s.

(a) When will it hit the ground?

    Solution. Since with and we need



This is precisely when or and thus the ball will hit the ground in 10 seconds.  

(b) With what velocity will the ball hit the ground?

    Solution. The velocity function is and so ft/sec is the velocity when the ball will hit the ground.

(c) When will the ball reach its maximum height?

    Solution. Since when or when The ball will reach its maximum height at seconds.

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Falling Body Problem
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
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