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The Height of a Falling Object Help

based on 6 ratings
By — McGraw-Hill Professional
Updated on Sep 27, 2011

Introduction to Finding the Height of a Falling Object

The height of an object dropped, thrown or fired can be computed using quadratic equations. The general formula is h = – 16 t 2 + v 0 t + h 0 , where h is the object’s height (in feet), t is time (in seconds), h 0 is the object’s initial height (that is, its height at t = 0 seconds) and v 0 is the object’s initial velocity (that is, its speed at t = 0 seconds) in feet per second. If the object is tossed, thrown, or fired upward, v 0 is positive. If the object is thrown downward, v 0 is negative. If the object is dropped, v 0 is zero. The object reaches the ground when h = 0. (The effect of air resistance is ignored.)

Typical questions are:

When will the object be ___ feet high?

When will the object reach the ground?

What is the object’s height after ____ seconds?

Determining When an Object Will Reach the Ground

Examples

Example 1:

An object is dropped from a height of 1600 feet. How long will it take for the object to hit the ground?

Because the object is dropped, the initial velocity, v 0 , is zero: v 0 = 0. The object is dropped from a height of 1600 feet, so h 0 = 1600. The formula h = –16 t 2 + v 0 t + h 0 becomes h = –16 t 2 + 1600. The object hits the ground when h = 0, so h = –16 t 2 + 1600 becomes 0 = –16 t 2 + 1600.

The Height of a Falling Object Examples

The object will hit the ground 10 seconds after it is dropped.

Example 2:

A ball is dropped from the top of a four-story building. The building is 48 feet tall. How long will it take for the ball to reach the ground?

Because the object is dropped, the initial velocity, v 0 , is zero: v 0 = 0. The object is dropped from a height of 48 feet, so h 0 = 48. The formula h = –16 t 2 + v 0 t + h 0 becomes h = –16 t 2 + 48. The object hits the ground when h = 0.

The Height of a Falling Object Examples

The ball will reach the ground in about 1.73 seconds.

Find practice problems and solutions at The Height of a Falling Object Practice Problems - Set 1.

Determining When an Object Will Reach a Specific Height

Example

An object is dropped from the roof of a 60-foot building. How long must it fall to reach a height of 28 feet?

In the formula h = –16 t 2 + v 0 t + h 0 , h 0 is 60 and v 0 is zero (because the object is dropped). The object reaches a height of 28 feet when h = 28.

The Height of a Falling Object Example

The object will reach a height of 28 feet after about 1.41 seconds.

Find practice problems and solutions at The Height of a Falling Object Practice Problems - Set 2.

Determing How Long or at What Time an Object Will Reach a Specific Height

Examples

Example 1:

An object is tossed up in the air at the rate of 40 feet per second. How long will it take for the object to hit the ground?

In the formula h = –16 t 2 + v 0 t + h 0 , v 0 = 40 and h 0 = 0.

h = –16 t 2 + 40 t

We want to find t when h = 0.

The Height of a Falling Object Examples

The object will hit the ground after 2.5 seconds.

Example 2:

A projectile is fired upward from the ground at an initial velocity of 60 feet per second. When will the projectile be 44 feet above the ground?

In the formula h = –16 t 2 + v 0 t + h 0 , v 0 = 60 and h 0 = 0.

h = –16 t 2 + 60 t

We want to find t when h = 44.

The Height of a Falling Object Examples

The projectile will be 44 feet off the ground at 1 second (on the way up) and again at 2.75 seconds (on the way down).

Find practice problems and solutions at The Height of a Falling Object Practice Problems - Set 3.

More practice problems for this concept can be found at: Algebra Quadratic Applications Practice Test.

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