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Falling Bodies Help (page 2)

By — McGraw-Hill Professional
Updated on Aug 31, 2011

Example 2

A body is thrown straight down with an initial velocity of 10 feet per second. It strikes the ground in 12 seconds. What was the initial height?

Solution 2

We know that υ 0 = −10 and that h (12) = 0. This is the information that we must exploit in solving the problem. Now

h ( t ) = −16 t 2 − 10 t + h 0 .

Thus

0 = h (12) = −16 · 12 2 − 10 · 12 + h 0 .

We may solve for h 0 to obtain

h 0 = 2424 ft.

The initial height is 2424 feet.

You Try It: A body is thrown straight up with initial velocity 5 feet per second from a height of 40 feet. After how many seconds will it hit the ground? What will be its maximum height?

Example 3

A body is launched straight up from height 100 feet with some initial velocity. It hits the ground after 10 seconds. What was that initial velocity?

Solution 3

We are given that h 0 = 100. Thus

h ( t ) = −16 t 2 + υ 0 t + 100.

Our job is to find υ 0 . We also know that

0 = h (10) = −16 · 10 2 + υ 0 · 10 + 100.

We solve this equation to find that υ 0 = 150 ft/sec.

You Try It: On a certain planet, bodies fall with an acceleration due to gravity of 10 ft/sec 2 . A certain body is thrown down with an initial velocity of 5 feet per second, and hits the surface 12 seconds later. From what height was it launched?

Find practice problems and solutions for these concepts at: Applications of the Derivative Practice Test.

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