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Chapter 2: Problem 67

A falling object travels one-fourth of its total distance in the last second of its fall. From what height was it dropped?

Short Answer

Expert verified
The height from which the object was dropped can be found by calculating the distance the object traveled in the last second of its fall, and then multiplying that distance by 4.

Step by step solution

01

Calculating Time

First, calculate the time it would take to cover the last quarter distance. Knowing that the object fell 1/4 of the total distance in the last second, assume this 1/4 distance as s, the initial velocity as 0 (since it's in the last second), and g as 9.81m/s^2 (approximation of gravity on earth). Instead of using the equation \(v = u + gt\), it can be rearranged to \(t = (v - u ) / g\) and because the initial velocity \(u\) is 0 due to being in the last second of free fall, it simplifies to \(t = v / g\).
02

Finding the Total Distance

Next, find the total distance s by multiplying the last quarter distance by 4. However, in order to do this, we need to calculate the last quarter distance. Use the equation \(s = ut + \frac{1}{2}gt^2\) (knowing u = 0 again) which simplifies to \(s = \frac{1}{2}g t^2\). Once the quarter distance is found, multiply by 4 to get the total distance.

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